But yes, a woman can have a penis, a man can have a vulva, hell very rarely people are born with something more ambiguous. Some people get surgery to have both, which is incredible. You sometimes hear cis women talk about how it would be cool to have a penis, which doesn't automatically make them a man. The association of sexual anatomy with gender only exists due to the dominance of cisgender people, which has been enforced very violently over the course of our history. Certain gatekeepy medical "professionals" will get arsey with you if you say you don't want bottom surgery, because they must uphold the cisnormative social order. It's harder to keep their strangehold on cishet gender, which helps feed the machine of capitalism with workers, if people are running around questioning the dogshit assumptions they have put in place. Society drives these cisnormative assumptions into you from birth, which is insidious and hurts people and is part of why that shit must be stopped.

Why is a penis inherently male? Just because most people born with one are men? Ridiculous; if the penis belongs to a woman, she is still a woman, and the penis is female, same in reverse for anyone with a vulva, and of any gender. You are not pretending to be a woman, if you say you are one, you are, regardless of what is in your pants.

As a footnote to all of this, read The Gender Accelerationist Manifesto which is an awesome synthesis of trans/queer theory and leftist theory. Great read.