Having the opportunity to learn and discover philosophy is in my mind a
I'm going to read your question not as a psychological one (that as "What would cause someone to feel inadequate or unworthy or learning philosophy?") but rather as a question about whether there could be good reasons for feeling this way.
Before we go on, an important preliminary: what I'll say is intended to be perfectly general and not to be a diagnosis of your particular case. Since I don't know anything about your case beyond the question I've asked, I couldn't possibly speak to its particulars.
As for why someone might justifiably feel inadequate, one obvious answer is that they might lack the requisite talent. For example: if someone paid for me to do a PhD in mathematics, I would feel inadequate for the very simple reason that I don't have enough mathematical talent to be a serious part of the community of students in a PhD mathematics program. And if it turned out that my being part of the program meant I was taking the place of someone with real talent, that would reasonably make me feel not just inadequate but unworthy. I'd feel guilty for making poor use of a scarce resource.
That would be a reasonable worry. But there's another kind of worry. Suppose I actually had real mathematical talent. And suppose that this got me into a math PhD program. On the one hand, I would be worthy of being in the program. But on the other hand, I might be aware that it wasn't just talent but also some measure of luck that got me there. In fact, it would be virtually certain that someone equally talented didn't get the opportunity that I got. That might make me feel bad. Indeed, it would probably be true that many people were all things considered more worthy than I, even though I met the (demanding) standard for being in the program.
Suppose all that's true. What should we say?
There's no doubt that our good fortune often involves a real measure of good fortune -- of luck. The same often goes for one's bad fortune. The world shows no signs of making desert and reward line up neatly and there's no reason to think it ever will. In some cases, the mismatch amounts to real injustice; in those cases, the right thing might be to something about it, even if that means giving up something we care about. For example: if you ended up in your place by way of a head-to-head competition with somebody who was clearly more deserving, that would be an injustice, and might make a case for stepping aside. But if the worry is more in the nature of existential discomfort about the general unfairness of life, it's not clear that there's anything to be done. You ask "Why should I get this and not someone else?" There may be no good reason. But if you stepped aside to have your place taken by someone no more deserving, that wouldn't right any wrong.
Still, the fact that you have this concern could count indirectly in favor of your having the privilege. If you get a good philosophical education, you'll not only be intellectually equipped to bring philosophy to a wider circle of people; you may be much more motivated to do so than others with the same skills. That may be the best way for you to think about your good fortune.