That many of us on this board find it desirable to reduce the number of abortions does not mean the government's compelling interest in providing contraception to women is rooted in reducing the number of abortions.
But whatever is the basis of the government's compelling interest in providing contraception to women, that same compelling government interest must also apply to men, else we do not have equality before the law. Are condoms provided to men at taxpayer expense?
I don't know how women access contraception at taxpayer expense; it might well be the case that those same channels are in fact available to men.
In the case of the ACA, an ACA-compliant health plan must provide no-cost preventive health services. These include such things as annual check-ups and children's vaccinations, but also include contraceptives. No-cost preventive services are assumed to be good policy because they prevent more expensive health conditions that the health plan would have to pay for. They are justified, in short, on the theory that healthier members mean health plans save money. In the case of contraceptives, the expensive health condition that contraception is supposed to avoid is childbirth.
Of course, since health plans don't cover abortions, the more cynical and cost effective step would be NOT to cover contraceptives, and direct women instead to the local abortion clinic!
Here's my bottom line - neither the right nor the left supports abortion per se (as opposed to the right, or liberty, to choose abortion). Conservatives counsel abstinence, or persuasion for pregnant women to do the right thing. Liberals counsel inexpensive contraception. I don't have any studies to cite, but I bet my bottom dollar that the left's approach prevents more unwanted pregnancies and abortions than the right's does. Of course, the true answer is to utilize all ideas that work, short of government coercion. Abstinence, persuasion, effective and affordable contraception - it all adds up to every child being wanted and cherished.