There is a saying among philosophers: "ought" implies "can." The application of this maxim to your question is as follows: It seems that anything that deserves to be called a "universal right" would be something that ought to be provided to everyone--no exceptions. But this could not possibly be true about education (or anything else, under the maxim) if the way the world is, as a matter of fact, makes it impossible, as a practical matter, actually to provide what such a "right" requires. So we might think about the question of whether or not there are people whom we simply can't provide with the resources necessary for the kind of education we might reasonably wish we could provide to everyone.

Now, I think the question of whether or not we actually can educate everyone will depend on facts about sociology, psychology, and economics that I do not pretend to know. But I am inclined to think that the idea of educating absolutely everyone to the extent we might wish to educate them is something we simply can't do. If so, I think it cannot be sensible to hold education as a "universal human right." Some things are very valuable desiderata; but not all of these are "universal human rights."

It might not disqualify you at some programs, but it will certainly count against you at most. The writing sample is the primary way of distinguishing applicants' philosophical talents, at least once they have been narrowed down using other criteria (such as coursework in philosophy and grades, letters--though for the competitive candidates, they tend to be equally gushing--and perhaps GRE). A 5-page sample is unlikely to provide evidence that you can develop an argument responding to a particular position that you have adequately and charitably explained. (Of course, Gettier's famous paper is quite short!)

I say all this with empathy--I was a philosophy minor (not major) and did not have a good, long piece of writing to submit when I applied to grad school. I had to use a mediocre, long piece, and was lucky to be accepted in the few places I was. But that was (too) many years ago when the competition was a little less fierce. I would try to work with one of your professors to develop one of your short papers into something more substantial (12-18 pages).

(On the other hand, people should NOT submit pieces longer than 20 pages.)

I am afraid your argument is a bit too subtle for the school, and one can see why. They are working on the principle perhaps that eventually something will click in the young man's mind and he will benefit from the "punishment". There is in fact some evidence that young offenders who constantly get into trouble often just stop offending, and it could be the punishment that does it. I understand that right now he does not see it as punishment, but hopefully the school is working on the assumption that one day he will, and perhaps they are right. Frankly, why should they care, if they can exclude an awkward student they will.

If you could make his exclusion less pleasant this would back them up and make him less ready to go for that option.

Let's suppose you say to me "How's your brother Paul?" I say "My brother is fine, but actually his name is Peter." Most likely that will be enough to convince you. And unless your reactions are rather unusual, you're likely just to ay something like "Oh. Yes. Guess I got mixed up." It would be really odd to call this indoctrination.

Or suppose I've been working on a budget and I send you the figures. You tell me that the total is off by $2,000. I don't believe you, so you work through the math with me, pointing out where I made a mistake. And I end up agreeing. Still nothing that seems like indoctrination.

However, those may not be the sorts of cases you have in mind, so try this one.

Suppose George thinks that women shouldn't be allowed to run for public office. Mary asks why. George gives his reasons, which reflect false beliefs about women's intelligence, emotions and so on. Mary engages him in a long, calm discussion, after which George agrees that his views reflected various kinds of prejudice and misinformation. George reconsiders his view and no longer says that women shouldn't be allowed to run for office. Still doesn't seem like indoctrination. Mary has persuaded George to change his mind by offering him reasons. She hasn't coerced him and she hasn't manipulated him. She also hasn't "prevented" him from expressing his former view except insofar as she's helped him see that it wasn't a well-thought out view to begin with.

If I enter into a discussion with you to try to persuade you of my view, then so long as I'm offering serious arguments and reasons, the word "indoctrination" seems very odd. The hallmark of indoctrination is intellectual manipulation that gets in the way of being moved by facts and reasons. And to censor someone is to prevent them from expressing a view that they actually want to express. If I've given up a view because I've come to see that it's mistaken, I haven't been censored; I don't want to express the view anymore.

Indoctrination and rational persuasion have something in common: when they succeed, someone's views change. But they also differ. Indoctrination doesn't show respect for the person it's practiced on; it simply manipulates them. Likewise, censorship and rational persuasion have something in common: when they succeed, some view that might have been expressed isn't. But they differ too. Censorship goes against the will of the person censored; rational persuasion engages their will.

All of which suggests some obvious final thoughts: if this seems reasonable to you, then you may no longer hold the view you started out with. But if it seems reasonable, I hope that's because it stands up to reflection. And if it doesn't, you're more than free to say so and say why.