Because the only way to truly understand a position is to put yourself through a crucible of alternative thinking.
If your idea survives, and your argument is compelling, you're likely basing it off of logic.
If you get destroyed and you can't make any salient points, you're either going to reexamine your position, or others will dismiss it outright for being so obviously based in illogic.
Case and point.
Another user got banned for throwing a temper tantrum after losing a debate where he claim Denmark brutally conquered Greenland.
This never happened, but he was insistent to the fact. After losing the debate, he threw a tantrum and got himself banned.
But at least three people were encouraged to research the material we debated on, and confronted him over his ignorance.
Three people learned something they wouldn't have known, as a result of our debate.
Will he continue to lie to people? Yes. Will they believe a word of it, now that there is such blatant proof he's wrong? I doubt it.
Debating is just as much about protecting others from propaganda as it is about winning an argument, at least for me.
I would pick many of these options if I could. Point is, intelligent dialogue just makes us better people all around. We are smarter in our beliefs and stances, we are more informed of what the other side thinks, and we're more prone to talking than to taking to conflict.