I refuse to accept "birthing person" as a name. It's a very passive label limited to an action.
We know women give birth. We know women get pregnant. We know that the impacts and implications resulting from pregnancy, miscarriage, labour and childbirth affect women for much longer than the action of birthing a baby.
So it very much is woman centred.
And for people who say "oh I don't mind using non sex specific language for this STUFF, it's more inclusive" you don't get to sell out an entire sex just to be nice. You don't get to tell others they are transphobes over this. Because it's not about hating trans people, it's about making sure the sex based care and issues are kept correctly labelled and termed so that we know what issues and care exist and can be taken care of.
I generally dislike companies like the Positive Birth Company anyway due to their completely unrealistic ideals of birth. You cannot positive think your way into the perfect birth. I have friends who were very badly affected by their labours and births because they thought affirmations would see them through and refused to consider going to a hospital for labour until they had to be blue lighted there due to the baby being in serious and prolonged distress. They had been told that they could manifest the birth they wanted. It was horseshit. They felt they had failed by having an epidural and stitches. Others felt they had failed by having a c section because it wasn't what they had planned.
So not only are companies selling the idea that you can deep breath and wish for the perfect birth, but that it isn't actually a woman's event, it's not centred around a woman.
Nope. Nope. It's literally a specific biological function of a woman. Doesn't matter how you dress or what pronouns you use or what surgery you have. Biologically if you can get pregnant you are a woman.