Yes, birthgiver indicates precisely what Mary did, she was the chosen vessel to give the physical birth to our Lord. That includes all the responsibilities motherhood implies. Quite frankly it would have been far easier for Joseph to walk away than Mary.
"Mother of God" implies Mary is was so much more than just a birth and care giver. Salvation depended upon Mary for she was the Mother.
Would you say Mary was sinless in contradition to Rom 3:23? I think you do get it.
birthgiver [of God] includes all the responsibilities motherhood implies "Mother of God" implies Mary is was so much more than just a birth and care giver.
I think this is still contradictory. Don't you? Or have I changed the meaning of your reply in condensing it?