I recently argued that economics could help evolutionary psychology explain why parents and their children disagree. If your actions have externalities for your siblings or other kin, the optimal choice for your parents' genes differs from the optimal choice for your genes.
But this story still seems helpless to explain all the times that kids ignore parental advice that really is in the kid's best interest, like "Don't run into traffic," or "Don't major in philosophy."
Once again, though, economics comes to the rescue. Suppose that 50% of parental advice helps the parent at the kid's expense, and 50% of parental advice actually helps the kid. Optimal kid's response: Ignore the former, heed the latter. But suppose we add a plausible catch: The kid can't tell the first kind of advice from the second. There's imperfect information: Parental nagging all sounds the same to him. By the time you figure out how to tell one from the other, you're a parent yourself.
What's a rational child to do? You choose an intermediate course of action. If there is a 50% chance that going to college is for your own good, and a 50% chance that it helps the family at your expense, parental nagging provokes roughly half the extra effort your parents recommend. (Strictly speaking, it depends on functional forms and what not, but you get the idea). The result: You follow some advice contrary to your own interest, AND ignore some advice that serves your interest. The higher the probability that your parents are putting your interests first, the milder these mistakes become.
If you're a parent, there are two strategies you could use to cope with this situation. The first is verbal inflation. If your kid goes half as far as you advise, double your recommendation. This might work for a while, but in the end, you'll probably end up with a bad case of rhetorical hyperinflation ("You must learn Latin! It's essential! Essential!"), and your kid will tune you out completely.
The second strategy is to build up credibility. Don't give into the temptation to exaggerate and manipulate. Don't be the dad who cries wolf. Then maybe your kid will believe you when it counts.