Can you birth a child and not be considered a mom?

Oly • SAHM who loves movies, nerdy games, music and cooking
I know you can still be a mom if you haven't given birth (adoption, have a misscarriage etc)
My question to you all is can you birth a baby and not be considered a mom? 
I read a story the other day about a girl who threw her baby in the dumpster and when she got caught she said horrid things about how it was gonna ruin her life and called the baby vulgar names. (A couple adopted it who can't have kids and loves the little boy more than anything now) 
But I don't consider that first girl a mom. I consider her ... A birth giver. What's your opinions?

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