First, we need to stop referring to abortion on demand as 'health care'. It may be 'health care' for her, but that's only half the story (literally). It most certainly is NOT 'health care for the life growing inside her, threatening to inconvenience her.
And please don't get me started on the whole 'it isn't fair that men get to have sex with no consequences' nonsense. I agree; it isn't fair. But you knew that going into the situation. If you didn't think about it, well, who's fault is that?
Second, if we're going to fight for a woman's right to make her own health choices, then it would seem logical (I know, I know - there I go again; acting all logical) that we should fight equally hard to protect the not-yet-born's health choices.
Finally, let's quit hiding behind the rare exceptions and call abortion for what it really is:
The Ultimate Selfish Act of a Woman
There’s a selfish man in the equation too. Men aren’t robots governed by their penises. We have free will and many abandon their children and chase orgasms instead of finding the right woman for a life-long partnership (i.e. marriage).