At least the abstinence programs teach some responsibility for your actions.
Hardly. In fact, did you know that states like Texas has the highest teen birth and STD rates? These are states that promote abstinence-only education, btw. So no, they don't teach "responsibility".
Furthermore, if they're not doing vaginal intercourse, they're doing oral or anal, both of which are also good ways to catch STDs without protection.
This is a divided subject, but I'm one who feels that just handing out condoms and giving birth control pills to middle school children is wrong. It puts peer pressure on these teens, and often pre-teens to have sex. "Well, they're giving us these condoms, so I guess they expect us to use them" is the mentality.
The condoms and the pills were only for those students who were
already having sex. They were not for those kids who are still virgins, unless the girl has female issues such as polycystic ovaries and severe menstrual symptoms (the BC pill isn't just for birth control, you know).
Furthermore, comprehensive sex ed teaches abstinence alongside contraception and abortion. Most parents want their kids to be fully educated about sex and all of the ways to prevent STDs and pregnancy should they choose to become active or not.