How do I respond to arguments for God being female?

Yesterday some Christian door-to-door ladies stopped my wife and me on the sidewalk, and invited us to their new church they are starting. We proudly informed them we are devout Catholics, and they started giving us “Did you know…” lines. The big topic was about God the Mother. They talked about how in Revelation, the mother was referred to as Jerusalem, and in Genesis, God says let us make man in Our image. Male and female he created them. Therefore female is also in God’s image, which means there is a female side of God. I reminded them that Eve was made from Adam’s rib, and that God, although referred to as Father, is not a specific gender (except as Jesus), in the physical (genital) sense of the word, and certainly God has female qualities such as compassion (just as men have a feminine side), but this does not mean that God is a woman in any sense. But their arguments were based much more in scripture than I was prepared to answer.
We shared email, so I want to be prepared to send her a well-thought-out response. Unfortunately, I have not been able to find solid writings about this topic. Have you heard this belief before? Can anyone help?

The following links should provide some helpful information for discussing God and gender. If you have any further questions, please contact Catholic Answers directly.

Recommended Reading:

Why is God referred to as a male?
Does God have gender?

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