Arguments aren't about winning. You will almost never convince someone your arguing with. Treat it more like a chance to better understand and strengthen your beliefs through putting them up to criticism and an opportunity to learn about a view you disagree with. I've found I have gained much more from arguments doing this. You can find flaws in your argument faster than doing it yourself, and you can fully understand the opposite opinion, it's line of logic, assumptions, and where it comes from, to truly understand why it is wrong. And you never know, that seed of doubt planted by a good argument could eventually change your or your opponents mind.

This is why online arguments suck. The other person often won't use critical thinking and just spout the same points regurgitated from their own little world, along with some logical fallacies to spice it up.