Let me tell you a story with an interesting twist...
So I was approached by an older man at the bar the other night and our conversation went like this: Man: "Hi, my name is ____"
Me: *pauses to assess situation* "Linda"
Man: *makes meaningless conversation*
Me: *politely replies while noticing that my male friends and the bartenders are now paying us very close attention* "Well, it was nice meeting you but I'm having a conversation with my friend"
Man: "oh okay." *wanders away and doesn't bother me the rest of the time I'm there*
That is how you handle rejection. He did nothing wrong by introducing himself and he left me alone when I made it clear I wanted him to.
However, my female friend had gotten the bartenders involved and they approached him after he left me and almost threw him out. My friend told me "Don't worry, I handled it."
No, she didn't handle it. I handled it. She actually made the situation worse. He almost got thrown out for introducing himself to a woman.
There is nothing wrong with approaching a woman and introducing yourself as long as you retreat when it’s made obvious they aren't interested. Treating me like I need protection is going to continue to teach men that women need protecting by other men because a woman’s own actions aren't meaningful enough to warrant proper behavior.
My claim on myself is enough.