There are several reasons I dislike these words. First, despite containing the word "people," these terms focus on body functions rather than the actual human person. Boys jeer at girls who are on their period. Men still make jokes in the workplace at times that a woman who is sharp towards them must be having "that time of the month" (notice that, even here, men are using a euphemism). Things like tampons were empowering because they allowed women to hide the fact that they were menstruating, which removed a tool that had been used to bully or humiliate women and therefore to gain social power over them. Calling women "people who menstruate" brings a physical vulnerability of women's bodies to the forefront of the conversation and to the forefront of the listener's mind, and therefore changes conversations to give us lower status. That is why it is dehumanizing.

Birthing people is problematic because it separates the physical (animal) (never forget that the idea is to position women as mere animals, in comparison to men who are the full and default humans) act of giving birth from the wholeness of the relationship between mother and child. Once I've given birth to my child, what am I then? No longer a birthing person, I suppose, but what? The fact that I gave birth to the child is unlinked from the fact that I am that child's mother. Terms like "birthing people" carefully slice up motherhood into functions that can be sold off or controlled from outside. And, as with "person who menstruates," it paints a particular picture in the mind (a partly naked woman, in pain, probably bloody, with her legs apart), and the goal of painting that picture is to disempower the woman in the social interaction of the person with whom she is talking.

Altogether, the big issue with redefining womanhood according to individual body functions, is that it attempts to separate each woman from the other. Little girls, adult human females, and postmenopausal women (even those without a uterus) have fundamental interests in common with each other. We have solidarity with each other (or, we should). But if we can't even speak about ourselves as a coherent class, then we can't organize or talk to each other about our common concerns.