Though I am not Jewish, I have a wonderful rabbi. Here's what he tells me about praying for the sick:
Whenever we pray for a sick person we say, "May God who blessed Abraham, Isaac, and Jacob, Sarah, Rebecca, Rachel, and Leah, bless and heal _____, the [son or daughter] of ______." The last blank is not the father. The sick person is always referred to as the son or daughter of the mother. We invoke the mother's name. This is based on Jeremiah 31:14-19.
[Check it out: it's the passage on Rachel weeping for her children.]
And so the rabbis remark on this passage that in the end of days when it comes time to redeem Israel, God will not listen to the pleas of Abraham, Isaac, Jacob, and Moses. Rather, what moves God most is the plea of Mother Rachel. This is based on the simple Jewish notion that what women and God share in common is the very custodianship of the sanctity of human flesh. Both are creators of the flesh. Men by definition are not. For that reason we pray for sick people in the name of their mother.
In case you're wondering, my rabbi is not worried about being politically correct: he's Orthodox.