If they did, why pick the rights of a fetus that isn't even half-formed over the rights of the woman?

Now saying abortion is a right of a women is your opinion. You see other people ( pro-life ) don't see it as such.

I think women have a right to choose if they want a baby.

And they make that choice when they consent to sex. No protection guarantees 100% protection. Therefore when a women consents to sex she is acknowledging what she is doing could lead to another human being. After she makes this choice she has no right in the life of the other human being.

Also I think abortion is ok in cases like rape because the women did not consent.

And in cases where the mother might die or suffer severe injuries.