When I was young, I was told everyone is unique and different. I take the word "different" as in some people like ice cream while others don't (is there any kids who don't like ice-cream?), or some are hardworking and others are lazy.
Somehow, there is deeper meaning in the word "different". I have a friend who can debate or disagree with me on every statement I made to him. Like whether Bill Gates is a generous philanthropist, is he doing more good than evil? Is Balian in Kingdom of Heaven a reluctant hero or pure evil in disguise? Is George Lucas a brilliant or lousy director? etc ...
On every idea that you think you are absolutely right about it, don't be surprised there are someone who totally disagrees with you. In fact, it is extremely difficult to get everyone to agree on an idea without a great deal of compromise and synergy.
All these while I seldom notice these differences among my friends, probably because most of them either agree with me or reluctant to engage in a debate with me. Those who engage in a debate with me give me some fresh idea, but sort of annoy me in the long term. Sometimes I even give up in a long debate as well, thinking "Well, we're indeed different. No point dragging it".
So, how difficult is it to be together with someone who is extremely indifferent from us? It can be annoying at times, but it does intrigue us as well. Should I choose a girlfriend who is indifferent from me, or someone more compatible? At this moment, I would say I still prefer compatibility, as there are much to be shared between us and having less conflict.