Closer to the subject at hand, the same logic can (and is) applied to contraception. Abortion has just gained extra weight in some people’s thinking.

But that's it exactly. The pro-abortion argument is a pro contraception argument. They want to normalize abortion as contraception. And they've largely succeeded.

To the point where they equate being "burdened" with a child as life-ruining, and having choice to undo that as essential to women's freedom.

Never once do they think that maybe if having a kid screws up a woman's life that means she never had freedom in the first place.