The only time I have heard the term "birthing People" was in relation the help.. such as mid wives etc.. but that may be so complicated that getting it into the heads of some people is not possible.. they may think men can have babies or some such foolish notions..
Isn't that why your church is against real birth control?
In a way, yes. But this is one of the rare examples of a subject upon which the church has changed its stance, at least unofficially.
Artificial birth control, which you ironically refer to as "real", is pretty much a non-issue now for most Catholics now that abortion is rampant. In fact most now endorse birth control as a prevention for abortion. As do you and I Bad Bob.