It isn’t stupid. It just doesn’t work. I don’t know when the first restriction on sex before marriage was put into place, but there was probably an instance of it two hours later. Thousands of years of human history, including when the penalty was much greater than today, didn’t stop premarital sex, so I don’t see why you think teaching abstinence only classes or restricting birth control to those who are married is going to reduce the abortion rate at all.
As for pro-life groups teaching birth control., perhaps we can call Catholic methods birth control, but that is pushing it. A while back the Times had an article on how pro-life groups were already moving towards claiming that standard birth control methods were dangerous, as a prelude to trying to ban them.
I doubt many if any pro-choice people are against teaching abstinence as the best method of birth control, but teaching it as the only method is a sure-fire way of increasing the number of abortions, which is something no one wants.