Why is it that men do not wear engagement rings? They propose to the girl, preferably with a pretty diamond ring which marks her as his, placed on the third finger, the one (supposedly) closest to the heart.

A girl with an engagement ring pretty much has a "Taken" sign on her forehead, warning off any other men who might want to pursue her.
why is it not "THE OTHER WAY ROUND TOO", let the men also put it on to scare other girls.