How do you deal with argumentative people?

It's hard - but disengage. Stop answering. Walk away if you have to. When someone's looking for an argument, the best response is to deny them.

I don't talk to them. I had a roommate like that. Whenever she started I abruptly went quiet and just stared at her with raised eyebrows. Then I turned my back to her and minded my own business.

I provide one or two pieces of evidence then I walk away

check and see if he/she is my boss then walk away

well.. haha, if the person is a woman I generally pass cuz there is no point, you'll always lose :) ..if a man, I give him a good shake

ignore asap

I just shut up. Let them have the petty win.

They can only be happy with that. A smarter man will learn and understand the mistake to make amends for the same.

None of us can always be right but we can accept our faults to be able to learn something.

I tend to avoid them altogether...no need to get involved with people who can't rationalize and respect what you have to add.