Perhaps someone will correct me if I am wrong, but it is my understanding that the Jews practice this tradition at least they did for generations. Perhaps that is why the Catholic Church did the same at one time. Nothing sinister about this IMHO.
Your intuition is correct. It's derived from synagogue practice of the (now) Orthodox Jews. I think they still maintain that tradition.
As long as the women kept the children on 'their side,' it was a GREAT deal for the men. The Ancien Regime did not have 'metrosexuals.'