I'm not sure how much sense this argument makes. Most of the big sports schools are public, and I'd argue the budgets for academics at public schools should come from the states they're in, not from donations. I don't think it's obvious that private universities are raising that much money from their sports programs, but I'm open to being convinced if you have sources indicating this isn't the case.
As an aside, I don't think telling people that they haven't thought of things sufficiently is a particularly effective way of convincing them. There are a lot of potential other reasons someone might not agree with your point of view, and it's a bit hypocritical to tell someone else they're "not thinking things through" when you haven't actually figured out the reasoning behind their opinions.
You're not thinking things through, or doing even the bare minimum research. Financial data on sports revenue for most colleges is out there for anyone who cares to look. It's not my job to convince you of anything, I'm simply telling you how it works.
As an aside, I don't think telling people that they haven't thought of things sufficiently is a particularly effective way of convincing them. There are a lot of potential other reasons someone might not agree with your point of view, and it's a bit hypocritical to tell someone else they're "not thinking things through" when you haven't actually figured out the reasoning behind their opinions.