I think that equality of opportunity is a tricky concept to deal with, and I'm not sure that even its advocates can really present a clear case on its behalf. The problem, as I see it, is that there is no thing that is "opportunity," such that we can somehow make sure that everyone has some satisfactory level of opportunity.
Further, it seems clear to me that certain opportunities are inherently tied to the kind of person one is. As a prospective philosopher, different things will count as important opportunities for me than would count for my good friends Gizelle, who has studied fashion design, Hogan, who is working towards his degree in landscape architecture, Eric, who is pursuing a job in chemical engineering, or Andy, who is looking for work in the public sector (trampling on my freedom!). Trying to accord each of us an equal opportunity would not simply be difficult; it would be an incoherent objective.
Further, the quality of an opportunity seems to be contingent on what someone will do with it. Two philosophy students could both be given a chance to pursue the same degree in the same school, only to discover that one of them could not comfortably keep pace with the rigorous curriculum, while the other breezed through her work without any trouble. Even though the program being offered to both was the same, it seems like we would want to evaluate the opportunity afforded to each differently.
So what egalitarians of opportunity seem to be committed to is some notion that we should all be granted an equal opportunity for self-realization, whatever form that might take. In this view, I don't think we'd want to confine ourselves to attempting to categorize opportunities by "number and nature," because ultimately those ideas are either going to be irrelevant (who cares how many different opportunities you have if the ones you want are available to you?) or circular (if you want to talk about "goodness" or "aptness" as being a part of the nature of the kinds of opportunities we want to provide for people, then isn't it definitional that we would want to provide them?). But the basic idea, I think, is not an unreasonable one: in a good society, we will all have an equal chance of living the kinds of lives that represent a Hegelian sort of ideal of self-actualization, where we are able to break free of the constraints imposed upon us by our material realities, in order to bring an order to our existence which reflects our true spirit and soul. Worded this way, it seems odd -- even vulgar -- to suggest that we should come out in favor of a system of social organization which affords such opportunities to some, but happily denies them to others.
A few problems arise, I think, in trying to apply the egalitarian framework just discussed to a system of social organization. First, it is unclear how one would want to administer the provision of these opportunities. Even if we pretended, for the sake of argument, that giving power to some people would not result in the kinds of exploitative and undesirable outcomes discussed by Public Choice economists and readily observable around the world and throughout history, it seems likely that providing everyone with opportunities would require some kind of knowledge about what kinds of opportunities would help individuals. But of course, this knowledge is not available to anyone, and attempting to gather it would undoubtedly be a Herculean task. In a post-scarcity Marxian paradise where everything is readily available to everyone at no discernible cost, it's clear that anything but egalitarianism would be crass. But in our world, the difficulty of knowing what things are actually necessary or conducive for individuals to lead fulfilling and meaningful lives represents a serious hurdle.
Complicating things further is the fact that the opportunities that egalitarians favor typically involve either the use of other people's property, or actual effort from other people. Providing these opportunities, then, would very often require that we make impositions upon people, either forcing them to do something that they did not choose to do, or using something which belongs to them without their permission (and in both cases, punishing them if they resist). I think you're quite right to notice that using someone's property is a very different sort of thing from coercing them into actively doing something, and so I'll try to discuss these kinds of impositions separately. But I want to defend the conclusion that it's not clear that these impositions would be justified in the way that egalitarians have in mind, even if we ignored the problems raised by knowledge problems and non-benevolent administrators of egalitarian programs.
I'm not sure what needs to be said in defense of the idea that we should generally not be compelled to do things for other people against our will. The obvious point is that this sort of thing is slavery. But I do think that the issue is a little bit more complicated than that. As others have pointed out, there are certain situations where withholding our effort from others would be morally horrifying. Peter Singer brings up the example of a drowning child whom we could rescue if we wanted to, and Peter Unger discusses a dying man by the side of the road who we could save if we only drove him to the hospital. In these situations, I don't think it's clear that we would defend someone who chose to let the child drown, or the mad die. And further (some libertarians have disagreed with me here, most notably Tony Carilli, for whom I still have enormous respect in spite of this position), I think that many of us would think it justified to use force if necessary to get someone else to exert this kind of effort if they refused to do so voluntarily (for example, if I couldn't swim out to the child, but you could, or I didn't know how to drive the car).
Nevertheless, I think it's clear that the sorts of situations that we discuss above are categorically different from those which egalitarians seem to think would justify coercion. If, for example, I chose not to hire a particular individual to work in my company, but my hiring him were necessary for his self-realization, would it be permissible to force me to work with him? One thing that comes immediately to mind in thinking about this question is that an important part of my life plan seems like it would be the ability to make that decision for myself. In our story, we are not assuming that this person is going to die, or lead a terrible, miserable life without my help (I will discuss this a little later on). We are here considering a scenario in which one person's life plans are to be coercively derailed somewhat so that someone else can have an opportunity that would be meaningful to them. Now on one hand it might seem that this would be only a slight inconvenience, and the decent thing to do would be to tolerate the guy. But I don't think that this is the kind of inconvenience we would be justified in imposing on someone; people should be free, I think, to decide how they want to live their lives and who they want to associate with. If that seems counterintuitive, though, I would be open to exploring the issue more deeply. So if we accept this idea, which I think makes a lot of sense, that we shouldn't be forced to go out of our way to help people who don't actually need our help, but would simply be made better off for it, then that seems like it throws a wrench in the egalitarian machinery.
But the egalitarian could rightly point out that in many cases, no one would need to be forced into doing anything as long as we could legitimately take stuff from some people and use it to convince other people to voluntarily provide the efforts and goods we want. As the discussion so far should suggest, this almost certainly wouldn't be possible in all cases: for some people, the opportunities that would really bring them fulfillment are unattainable without the use of coercion, and sometimes they're simply unattainable. And it's a really important problem for egalitarians, I think, to address the question of whether these out-of-luck individuals would lead us to call into question the acceptability of our own opportunities. But that's another discussion. For our purposes, it will be sufficient to note that if we are hesitant to use blatant coercion (where we actually make people actively do stuff) whenever necessary to bring about the opportunities demanded by a consistent egalitarian position, we will need to accept that some opportunities will be unprovided for, and we will have taken an important step in the direction of a libertarian point of view.
But for many circumstances, if we could only legitimately take a bunch of stuff from some people and give it to other people (without forcing anyone to do much of anything, except maybe having to go through the hassle of filling out tax forms and mailing checks and whatnot), we could go a long way in ensuring that people had the opportunities that an egalitarian framework would desire. So then the next step in my argument must be to show why these kinds of takings would be ethically questionable. To do so, I'll try to take a rather unconventional route for a libertarian account: straight through the philosophy of Karl Marx.
In his essay, Estranged Labor, Marx argues:
It is...in his fashioning of the objective that man really proves himself to be a species-being. Such production is his active species-life. Through it, nature appears as his work and his reality. The object of labour is, therefore, the objectification of the species-life of man: for man produces himself not only intellectually, in his consciousness, but actively and actually, and he can therefore contemplate himself in a world he himself has created. In tearing away the object of his production from man, estranged labour therefore tears away from him his species-life, his true species-objectivity...
Now, it's important to note that Marx's account is fundamentally grounded in his acceptance of the labor theory of value, which leads him to believe that in laboring, we directly transfer value from ourselves to the objects which we produce. Accordingly, we need to divorce the element from Marx's account which implies that we are literally taking objectified value from someone by taking from them the object of their labor. In severing this connection, we may also notice that Marx's point seems to go beyond simply the products of our labor. What's left seems to be the basic idea that a central part of a person's formation of her identity and ordering of her reality involves the use and manipulation of material objects. By tearing away these objects, we dispossess individuals in an important sense of the things which give their lives meaning -- of the things which compose their reality, and represent their attempts to create a world in their own image.
On this basis, then, it seems fair to say that we must be extremely hesitant to advocate taking individuals' possessions. To justify such an invasion of someone's personal space -- to interfere with their projects, as many say -- one would seem to need a reason for their actions similar to the kind of reason one would have to provide for coercing someone or harming their person. Again, this is not to say that such a justification could not be found, or that the right to one's property is absolute (or even that the right to property should be understood in the way that libertarians often think of it). But it does seem to me that equalization of others to oneself fails to provide the kind of compelling justification that we would want before we condoned the taking of one's property. Again it will be helpful to note that while an individual's interest in a particular piece of property may be small, it seems reasonable to think that we have a serious interest in not having our stuff taken.
What we're left with, I think, is a basically libertarian way of looking at things. If what I've said so far makes sense, it seems like we would have a reasonably good reason to hesitate at advocating the coercion of individuals and the theft of property in order to equalize opportunities, even if such a thing were possible and we knew how to do it. But on top of that, I'd add another layer of skepticism arising from the fact that it's often unclear what equalizing opportunities would entail, and sometimes when we do know what it would take, the actual equalization would be impossible or tremendously difficult. Further, putting a group of individuals in charge of actually affecting the provision of these opportunities seems like it would open the door to gross abuse and corruption, in many cases bringing about worse opportunities for the very people the system was meant to help.
You'll note that nowhere in there was an appeal to "self-ownership" as such, or to the "Non-Aggression Principle," as commonly understood. I did rely heavily on the idea that we should be free to pursue fulfillment and meaning in our lives without the interference of others unless they can provide good reasons for their actions, and I did suppose that the mere fact of inequality is not a compelling reason to interfere with this prima facie right to self-determination, especially in light of the knowledge problems and Public Choice problems faced by would-be equalizers. But I think that those ideas are appealing to most people, and don't put me too far off the reservation as a libertarian wingnut.
So Neverfox, hopefully that functions as a basic response to your question. I'm sure I missed something along the way, and I anticipate that you'll have some objections to some things I said, so feel free to ask any questions that come up.