I did think this was a bit too long to be a comment, so I thought I'd make a response-post. Here's my opinion on the issue:
The thing about this issue is that it's not an easy question to answer.
Women do need control over their bodies; that much is true. But what if a man doesn't want a child? Should he be forced to accept her choice? The answer I come to isn't an easy one to swallow, but it's one that I'm sure many other biological women share.
Yes, he should have to accept her choice.
The situation you wrote about, Pluto, is a rather common situation in the realm of pregnancy and abortion; but something you may not realize is that women have to live with whatever choice they make for the rest of their lives. Men? They can, and often do, run. (Keep in mind that my father did that, and I feel no bitterness towards him for it.) I don't believe that he should have to pay that child support - if she refuses an abortion, it really should be her responsibility to take care of it in whichever way she sees fit - but he should not have the power to tell her that she should get an abortion if she believes it's wrong.
I say this as a pro-life advocate currently in a long-term, possibly-reproductive relationship with a pro-choice advocate. (The girlfriend and I are both pre-hormone trans people, so we are reproductively capable.)
Equal rights? No. Men should not have equal rights to another person's body. He should, however, have the right to be as involved in the child's life as he wants; a man should not be denied visitation or custody because a woman says so, and a man should not be forced to pay for a child he tried to convince his lover to abort. He shouldn't have the right to tell a woman what she should do, but he should have the right to be as involved in it as he wants (with due legal process).
Just my two cents. I'll probably write another post about sexual rights later.