When I googled it, this is what I found: “According to Chabad.org, a site that reports on Judaism and the Torah, the “ladies first” rule is a very old tradition. The story goes that when Moses was instructed to inform the people of Israel about the Torah, he was told to “speak to the house of Jacob, and tell the sons of Israel.” Since the house of Jacob appears first in the instructions, and it refers to women, the theory follows that Moses had to speak first with the ladies. Probably a smart political move.”
I don’t know if this true or not, but it was certainly an interesting svara.