I certainly agree with the goal of giving individuals their freedom and to have the right to act in an atypical way.
But let's keep a hold on reality here. Women carry babies, not men. Women breastfeed, not men. Women have higher trait agreeableness and exhibit maternal behaviors at all ages in all cultures ever [1]. These aren't "gender essentialism", they're biology.
There is a difference between saying "this kind of person usually does this" and "this kind of person must only do this". The first is often correct, the second is the one that's problematic.
Women will always be more linked to children, and that's fine. We shouldn't try to hammer humans into an ideologically-defined artificial shape, even if it's "equal". That's a recipe for great sadness. Just let people be.