It wasn't illegal anywhere in the US until the late 1800's when religious groups thought women showing more than their hands and head would lead to the temptation of men, and therefore impure. This was spread more by church than the state and surprisingly most states its still legal unless it upsets someone which then makes the legal act of topless the crime of public indecency. Stupid huh?
Because it's overexposure of the female body. If women were allowed to go topless in public, it would be evident that our society has reached its all time low.
Even in some countries where women are allowed to go, there are some social situations where a man can do it but a woman can't. Then there are some countries that have allowed it for so long, but the approval by other women towards women who go topless is declining.
You've obviously never visited Bondi Beach or you may not have asked this question. There are lots of beaches in Oz where topless is sanctioned.
Of course, women aren't the only people with boobs. In the BBC series, Rebus, a middle aged detective inspector was hitting on his attractive DS. She rebuffed him, saying, "I prefer to go out with men whose breasts are smaller than mine."
But male or female, ageing threatens the same fate for all: Our chest will fall into our drawers. When that happens, both genders would do well to cover up. :(