Nah. You just don't notice because women wouldn't be so boorish about their objectification.

That's another part of this. Men objectify women, in part, as a perdoemance of masculinity for other men. It's chest thumping.

A woman objectifying a man has no need to prove her femininity to another woman so the objectification isn't going to be loud and obnoxious.

Women do, in fact, objectify men. But men don't notice most of the time, or don't recognize it for what it is.