Closed minds and disrespect for those with differing opinions is what divides people; nothing else, not race, class, or any other superficial dividing line.

When someone says to you, during a discussion, that "we simply should agree to disagree," they are actually saying that they can't rebut what you just said but they're not going to concede the point either. They can't admit to themselves that you're right, they don't respect a differing opinion, and they can't accept that they're wrong. That would require re-thinking their entire world view.

If you suggest to someone agreeing to disagree, look inside yourself.