Why is the Catholic church called "Mother Church"....because of the belief in Mary as a Godhead with Christ?
Because there is a relationship between man and God and man and Church that parallels the natural nuclear family. God is the father, the Creator, Law Giver, Protector, Provider and Judge. The Church is the mother. Its role is to nurture, educate and serve the family of man.
And out of all that you got "Mother Church"? What does a mother do? I think your answer is there.
Pretty much the same reasons Russians have traditonally referred to "Mother Russia" and Germans call Germany the "Fatherland"; the same reason one refers to one's "mother tongue". In fact, the same impulse with an ironic twist produced "Ma Bell."
The second part of your post demonstrates only ignorance on many levels and is best ignored.