Abstinence only works if you can convince people to stick to it...
I don't support teaching "abstinence only", although if people want to teach their children that it is one method of avoiding *insert problem with sex here*, then I would be fine long as they also teach the alternatives too. Parents should at least tell them about condoms, if only to give them a contingency plan should their abstinence plan fail (after all, you are dealing with hormone driven teens here).
But hey, we live in a free country, if parents want to teach abstinence only that's their choice.