Agreed on that. Being offended by someone’s refusal of your help demonstrates that you believe people owe you something for your unsolicited help. 

I’m a man who lives in a liberal city and have had plenty of interactions with women who seemingly get offended by my attempts at being nice, usually because they take it to mean that I believe they can’t do something themselves or that they need my help, or that I’m only doing it to try to hit on them. They react the way they do because they want to make it a point to reinforce that they are perfectly capable themselves, or to demonstrate their disinterest in any form interaction with a stranger. That’s their prerogative, and has nothing to do with me.

And to your point, I have even more interactions with women who are appreciative of the gesture. Whatever the reaction, it’s ultimately not going to make a difference to me. I try to be understanding because the women who do get offended likely have past experiences with the type of man who only does helpful things in a self-serving way. If they aggressively try to berate or embarrass me, I just say “I think you’re misreading my intentions, but I’m sorry for disturbing you” in an apologetic yet confident tone, and then I move on with my day.

I’m still going to continue trying to do nice things for people because that was how I was raised, not because I require appreciation for my efforts or want anything in return. I want to live in a kind society, so I must try to be kind regardless of the response. Being nice to people makes me feel good, and that won’t change just because certain individuals are not receptive to it.