I believe education is the best possible gift a parent can give their child and if they have the ability, they should pay. Mostly because if they have the ability, then there is a good chance that they’re not going to be able to go to college because it’s grossly expensive in this country.
I also believe the student should work and provide for their own day-to-day expenses.
On a broader level, I believe it is society’s job to ensure that we have a highly educated population and thus our public colleges and universities should be free to students, provided they meet certain expectations. That isn’t the reality that we live in though and so I stick by what I said at the top.
ETA: My parents didn’t pay for my college because they couldn’t. We were dirt poor. So I worked full time (cobbling together multiple part time jobs) while at school. I’d be lying if I said I wasn’t bitter sometimes but I never thought my friends who didn’t have to pay were spoiled. They were fortunate. I was’t bitter ~at them~ I was just bitter about the situation. (Many of these people are still my best friends, several years after undergrad. I didn’t let it affect our relationship since it was my problem, not theirs.)