I think the math is pretty simple. Birth control is cheaper than abortion, and both are cheaper than raising a child. I don't need a study to tell me that it's far cheaper to give out free birth control now than to support those welfare babies for 18+ years, not to mention that may of those welfare babies will be the welfare parents of the next generation. So if you are of the opinion that it's the duty of society to prevent the suffering of their fellow man the this is probably the cheapest way to do it.
Now if you're of the opinion that other peoples suffering is not your concern then it make perfect sense to not want to have to help pay for another program aimed at preventing more suffering.
Probably what would be the best for society in the long run would be to let those that can't support themselves wither and die, but I'm not sure I want to see starving people dying in the streets.