No. What GP is saying is merely that being capable of childbearing obviously requires female biological sex. But the implication doesn't have to go in the opposite direction for it to be true.

Another example: the only vertebrates that can fly are birds(ignoring squirrels and weird fish). That's not equivalent to saying that the ostrich is not a bird.

Flying vertebrate => bird

Bird =/> flying vertebrate

> Applying this definition strictly means woman who aren't able to bear children are not women.

Not quite sure what the commentor you are replying to means by the social part but they didn't state that giving birth => woman is a 2 way implication.