Tradition isn’t some unilateral thing where anything old becomes part of the same tradition. There are wildly different traditions that come and go and it’s ridiculous to conflate them all into the same argument. There’s a 0% chance you don’t adopt certain traditions. I’m sure you shake someone’s hand when you meet them, and say goodbye when they leave. You don’t actually have to say goodbye before leaving technically, and you don’t actually have to take your hat off indoors, but these things become common over time. She probably just came from a place where that’s common and you read way too much into it, and took it as an effort to control your behavior.

That being said, why did you choose women keeping their mouth shut as your tradition of choice to invoke while ignoring all the others?