TL

“Here head connot mean ’source’, because source is the translated word for heads(plural). The singular is translated ‘mouth’. So should we say the man is the mouth of the wife?”

Not mouth as in what one speaks with, but like mouth of a stream as in origin. 🙂 And the first man was indeed used to become the origin of the first woman, the material out of which she was taken.

And FWIW, you have not by any means proved that ‘head’ always meant authority when used between people. Metaphors are not like that. One can make a metaphor out of anything from many different angles. As was noted, fire and water both have been used in a multitude of different metaphors with different meanings.