Yes, we can agree he benefits. But the way you're using profit is not the way he's using profit. He's using in the strict accounting sense. You're using it in a very general sense.
You're arguing apples and oranges. Of course he pesonally "profits" but he was talking in a sense of not for profit organizations and for profit organizations. There's a difference and deliberately trying to find fault with him by arguing a different argument does not make you look like you know what you're talking about.
If you want to argue like you just did, then you could say every athlete gets a profit by getting their tution paid. That's a benefit that can be put in monetary terms as well.
If you want to argue like you just did, then you could say every athlete gets a profit by getting their tution paid. That's a benefit that can be put in monetary terms as well.