How come all (or the majority, if not all) women wear their wedding rings but for men it seems to be optional?

Why do women all wear their wedding rings proudly, and for men it seems like many do not? are men trying to advertise themselves as available in case something interesting comes along? I thought of this question when someone else wrote that she asked a guy out for coffee and he told her later that he was married, yet he did not wear a ring.