Rasul Allah (sal Allahu alaihi wa sallam) said: "Whoever does not argue when he is in the wrong will have a home built for him on the edge of Paradise. Whoever avoids it when he in the right will have a home built for him in the middle of Paradise. And whoever improves his own character, a home will be built for him in the highest part of Paradise."

[Tirmidhi]

Arguing with people is strongly discouraged in Islam. We are to state our point of view and then leave it at that. Nor are we to involve ourselves in matters that do not affect a person's deen. Note that a person is to shun argument whether he is in the right or whether his stand is wrong. Both get houses built for them in Paradise. But since the person who knows that he is right finds it more difficult to leave the argument and let things be, he/she is promised a greater reward.

Arguing with people rarely gets anyone to change their minds. It usually only produces defensiveness and creates ill feelings between people. The issue becomes a matter of one's ego and makes it more difficult for a person to change their stance. Allah (subhana wa ta'ala) loves to have Muslims live harmoniously with each other. Try this hadith out in practice, and you will see that your relations improve with people and that you have greater peace of mind.