It starts with the Halachic prohibition forbidding physical contact between members of the opposite sex. This prevents handshaking between the sexes in the frum community. Then once we're all accustomed to the "no handshaking with men\women," rule, we often just forego handshaking altogether.
It's all pretty simple until you take it out of the frum world where no one else is aware of this "secret" to handshaking. When a frum person is out in the secular world, they're faced with the decision of how to avoid handshaking with member of the opposite sex without appearing rude or insulting.
Most guys are fine when I tell them that I don't shake hands with men. I've only had a few instances where people have taken offense to my "no handshake" deal. I've heard of people getting highly insulted and I've never understood it. So I don't shake your hand - what's the big deal?
My sister was scolded by an employee in a store she was patronizing for not shaking hands with him. Needless to say, she hasn't gone back to that store.
I had a black guy reply, "I'm a person too, you know," when I excused myself from shaking his hand. But when I explained to him that it was for religious reasons, he seemed to feel better about it.
It occurs to me that some people might find my, "Sorry, I don't shake hands with men," thing sexist. What do you think?