In general, I'm sure mothers and (especially) fathers don't like their daughters knocking boots because they don't like the image of their princesses being sullied. But's let's also realize that, practically speaking, teenage sex carries risks of pregnancy and disease that are deleterious to the regimented education plan the average teenager must complete in order to emerge equipped for the adult world. I believe, on some level, parental support for discouraging teen sex is fairly rational risk-averse behavior.
Suppose we attempt to analyze the psychology of dear ol' Dad. Assuming he is enlightened enough to allow his girl to ultimately make her own decision about keeping the fetus, there is a chance his teenage daughter will be burdened with an infant. No matter what course of action he chooses to take, the process exacts a cost on him (not to mention his daughter), whether that cost is putting money and energy into helping raise another child as his daughter finishes high school, losing an investment in his daughter's future as her college plans are compromised, or going through the emotional trauma of scenarios like the adoption process or heartlessly booting the girl and her offspring out of the house if she is 18.
Morality aside, there are two reasons why Dad might be hesitant to trust a largely approving but instructive sex-ed atmosphere. First, such a program places weight on the informed cognition of the teen. Debbie just forgot to feed the dog for the third time this week and made her mother cry just because she was pissed about a text message her girlfriend sent her. Is she mature and reliable enough to be trusted to use a condom or take the pill? to not use sex as a ploy? One dumb, very teenage lapse in memory or prudence and Daddy has to re-balance the family budget.
Second, kids really do listen (somewhat) to their parents regarding right and wrong, especially if they respect them. I remember the whole Nature v. Nurture war from the 90s, sure, but I don't reacall the consensus. In any case, why not hedge your bets if you're Dad and make public your preference that she wait? Dad should also keep in mind that teens are not the best at moderation, so a green light for responsible, deliberate sex might actually just push the transgressive boundaries further out to drunken hookups that may or may not include contraceptives.
Age of consent law, aside from being selectively invoked as a way of keeping creepy old men away from softheaded girls, reminds us that teen pregnancy inflicts collateral damage on parents. Broadly speaking (and I understand case-by-case this is horseshit) the idea that a teenager is not mature enough to decide when she's ready to copulate is an inductive conclusion drawn from the fact that a teen girl is not mature enough to provide for herself.
