It was also that men were seen as interacting intellectually and sexual desire was associated with women.

I wouldn't be surprised if it was partly due to men not being very involved in the domestic world. Like it makes sense, so much of expectations on women even today revolves around children, so a stereotype that women are horny as fuck as well makes a certain sense to include there.

Though I'll admit I'm thinking of Greece right now and this stereotype may have been one that didn't spread to Rome.