I don't think observing correlations is INHERENTLY sexist; it's the context which usually provides the implied moral/ethical/whatever judgment. In this case, I think there's probably a connection to toxic masculinity, which actually is sexism, while pointing it out is not.
But the husband isn't just PRIDEFUL, he's talking about refusing on behalf of his son. This isn't like not letting someone buy your kid a sportscar, or an ipod, or whatever, because the kid definitely IS going to college and definitely DOES have to pay himself if he wants to go to *prestigious-school and therefore has to choose now as a teenager if he's willing to gamble decades of debt for the reputedly better education and likely better opportunities it leads to! Imagine being this kid and finding out LATER that your dad turned it down FOR you and that's why you're a hundred thousand in debt, or that's why you couldn't go to your #1 choice school?! If he's applying to college, the kid is likely no longer even a minor! Fully legally responsible for financial debts but unable to accept financial gifts because Daddy's masculinity was threatened! Just... YIKES.
Re: two thoughts
But the husband isn't just PRIDEFUL, he's talking about refusing on behalf of his son. This isn't like not letting someone buy your kid a sportscar, or an ipod, or whatever, because the kid definitely IS going to college and definitely DOES have to pay himself if he wants to go to *prestigious-school and therefore has to choose now as a teenager if he's willing to gamble decades of debt for the reputedly better education and likely better opportunities it leads to! Imagine being this kid and finding out LATER that your dad turned it down FOR you and that's why you're a hundred thousand in debt, or that's why you couldn't go to your #1 choice school?! If he's applying to college, the kid is likely no longer even a minor! Fully legally responsible for financial debts but unable to accept financial gifts because Daddy's masculinity was threatened! Just... YIKES.