If you listen long enough, you wonder whether there is really such a profound disagreement about what parents want for their children. Culture war by its nature pours salt in wounds, finds division where there could be common purpose. Purity is certainly a loaded word--but is there anyone who thinks it's a good idea for 12-year-olds to have sex? Or a bad idea for fathers to be engaged in the lives of their daughters and promise to practice what they preach? Parents won't necessarily say this out loud, but isn't it better to set the bar high and miss than not even try?
None of this purity ball stuff has anything to do with the question of whether "it's a good idea for 12-year-olds to have sex."
Generally our culture has a tremendous fear, almost revulsion, of the idea of female sexuality and sexual desire. Much of that is channeled to and projected onto teen females, where all sensible people agree that maybe it's not such a good idea for them to have sex for reasons they can't quite articulate but can usually be summed up with "if you were a parent you'd understand." I'm not a parent, but I was a teen, and my opinion is that on balance the problem isn't that teens are having too much sex, it's that they aren't having enough. That's somewhat of a joke, as the issue isn't how much sex they're having it's about having an informed and healthy attitude about sex and sexual desire so they can make their own choices about what's right for them. But demanding abstinence, especially when cloaked in morality, causes people to grow up with messed up attitudes about sexuality.
And, no, 12-year-olds aren't teens.