In most cases, arguments are meant to be persuasive.  Take a moment to think about that.  How persuasive is an argument that automatically makes the other person wrong?  Are they going to be receptive to your point of view? What are you really trying to accomplish by directly challenging another person?

When you do challenge another person, are you ever satisfied with the outcome?  Or do you feel vaguely angry that they didn't "get it?"  Isn't it true that the arguments just go on and on and finally move on to another subject?

How do we break out of this cycle?  Here's some hints:

Avoid talking down to people.  If you take a stand on a controversial subject then statements such as "I think . . ." and "it's my opinion that . . ." grease the wheels of discourse and allow people absorb your opinion even if they disagree because hey, it's just your opinion.  Confrontational language does nothing to make people receptive to your point of view.

"I disagree" along with a rational explanation is also recommended.  Of course, you'll be required to provide a rational explanation.  "Rational" in this case is defined as an explanation that would make sense to the person you're disagreeing with.

Which brings up another point:  If you're never wrong, you're always wrong.  You have to give ground occasionally or risk losing the respect of people you're arguing with.  Ask yourself, what do you think of the opinions of other people who can never give an inch?  Do you respect them?  (Hint, the angrier they make you, the more likely it is that you're one of them.)

If you're confronted with people that you don't respect, don't respond.  In a mud fight, everyone looks the same.  I know that it's annoying to let a completely stupid asenine comment stand uncontested, but I guarantee that responding won't make it better.  Unless, of course, you like pointless, never ending arguments.

In conclusion, no matter who you're dealing with, be polite, courteous and respectful of their opinions.  Even if they're attacking yours like a rabid pit bull.  Napoleon said it this way:
"Never interrupt the enemy when he is making a mistake."