If she owns it why is the man then responsible for child support if the woman wants to keep the baby an the guy doesn't?
Because his responsibilty is to the child. Not the mother. If the child exists, the obligation to the child exists.
With that obligation for mother and father always being equal. Either they both of that obligation, nor neither do.
The mother can decide to not be responsible for the child, via the abortion.
In which case neither she nor the man are responsible for the child. Their obligation is always equal.
Again, if true equality between the sexes is desired, why does a woman have that ability, and not a man?
Because he's not carrying the child. If he wishes to carry the child, he gets that choice for his own body. If she's the one carrying the child, she gets to make that choice for her own body
Do women need some sort of special protection?
From a man MAKING her carry a child or MAKING her abort?
Nope. She is the one that gets to control the use of her own body. Just as the man is the one that gets to control his.
Their control over their own bodies are equal. Just as their obligation is equal. Either they are both responsible, or neither are.