Folks give birth without becoming a mother and one can be a mother without giving birth.

Surrogates exist, for example. Folks give infants up for adoption. In this case, you can wind up with a mother who didn't birth the child and a person who gave birth, yet didn't actually become a mother except in a loose sense of the word.

On the sadder end, stillbirths still happen and society doesn't really consider this person to be a mother. (I'm personally fine with whatever the parents choose to be called).

There's always more complexity than you know. There are trans men with wombs who give birth. There are are surrogates. There are 1000 other situations that I don't even know about. The law says "person giving birth", and I like that choice of wording. It doesn't exclude someone who is in a new, unexpected situation.

Just the same, the law says that the two parents can share the weeks of work off, not "mother and father", as that's clearly not always going to be an accurate representation.

It's not political correctness, just accuracy in terms.

It could also be father, stop assuming genders!