Why does Christianity not accept the claim of the muslim or the mormon?
Because their beliefs are counter to the Bible.
Roman catholicism's title, "Mother of God", is not in accord with the Bible as noted in my previous post.
Apples and oranges. I am not asking you to accept our beliefs but only what we mean when we, Catholic CHRISTIANS, say "Mother of God." We do not mean the mother of the Trinity or the mother of Jesus' divinity, only the mother of the one divine person, Jesus Christ. To imply that we do otherwise is to bear false witness to our beliefs. Or are you only interested in winning cheep debating points?