I've never won an argument

It's true, I haven't. It's hard to win something you've never played.

I avoid them. Like they were TSA pat-downs.

An argument is defined as an oral disagreement, which basically means: you see it one way and I see it another.

Why on earth would I change my mind to yours, or yours to mine, when we fundamentally disagree? It doesn't happen.

Sure you could try to make it happen — maybe with force, or with bribe, or by opening and closing an ironing board over and over again [that would be aweful] — but at the heart of the matter, the belief didn't change.

A man convinced against his will, is of the same opinion still.

In reality, both are likely right; for different reasons. And this may be because:

The things one person has been exposed to in their life has led them to see the world as x;

while the things the other has been exposed to has led them to see it as y.

And asking either to change their mind is like asking them to erase their entire history.

Not to mention, emotion gets tossed into it, which usually creates a downward spiral of defending opinion — often for the sake of saving face. And at this point, you aren't even arguing the topic any longer; you're just trying to win. 

So in this situation, I find it's best to avoid all of that, and instead, try to focus on the points that are mutually agreed upon.

Essentially, I'm suggesting a preemptive compromise that allows both parties to feel they have not conceded; and that they [and their respective opinions] are equally important; and that they both have won.

So how do you do that?

To preemptively compromise, you must first agree to not argue points, but rather discuss your opinions in detail. You then need to find the common ground on which you DO agree.

How do you figure out what you DO agree on?

The easiest way is to ask why(?). Why do you think x? Why do you feel y? Explain your reason(s) for that (those) position(s).

Eventually you will begin to unravel the points you can agree on.

Maybe you agree on the outcome, but not the means -- so you can focus on finding the appropriate means.

Or maybe there are points on one side that may not have been considered on the other; you can focus on those.

Asking why(?), and gaining an understanding of what is fueling the other's opinion, will help lead you to a reasonable preemptive compromise.

Then there is no winner and loser — there are two winners. Like two Charlie Sheens.

And most importantly you can avoid the time-wasting argument all together. And do something more constructive like arts and crafts or play the guitar.