I think it's dehumanising despite a "person" being human. Just because other terms might be more dehumanising, it doesn't mean this term is not.
As PP said, the "birthing" aspect reduces the mother to a bodily function. This is problematic in a hospital environment where patients already often feel somewhat dehumanised, as if they are a body on a conveyor belt of processes over which they have little agency. Women and black people in particular face greater risk of experiencing medical negligence, so this term works against them.
The other aspect of the term which is dehumanising is the removal of the word "mother". We live in a patriarchal world where most families take the male surname and most men earn more than their female partners. A world where the kind of care that is predominantly done by women is utterly devalued.
One small truth in the midst of this is the fact that if you are a mother, when you were a baby growing inside your own mother, the eggs that became your future children also grew there.
I find that a beautiful thought. All of us connected to our grandmothers like this, stretching back through time. A small female truth that isn't declared with a name and can't be influenced by money or violence. What did those mothers of the past have to endure to bring the lives into this world that eventually became your life?
It will go on being true, of course, but it is a truth that gets obscured when the word "mother" is removed.