I think something people are missing in this thread is the distinction between a conflict and a combat.
A conflict is when at least two people want things that can't be fit together - "Give me your cash!" "No, I want the cash, too!" or "The PM has ruined the country, time for a new PM," "Okay but only if he's from my party!" "No way!"
A combat is a violent way of resolving that conflict.
It's quite possible to have constant conflict without any combats. For example, here on this forum we're often arguing this or that point - we're having a conflict; we try to resolve this conflict by means of discussion and argument. It's not less interesting a conflict simply because we're not using swords or firearms (though sometimes I think... no, forget that I brought it up).
In a roleplaying game, one of the things which is interesting is the conflicts which arise, between NPCs, PCs, between NPCs and PCs, between love and duty, honour and reward, and so on. Some of these conflicts can be resolved by combat, and combat itself is exciting and fun (at least when it's only roleplayed). But they need not be resolved by combat. Sometimes just the threat of combat will make the other guy back down, and sometimes it needn't even be brought up, things can be resolved by negotiation, bribery, blackmail, and so on.
It's not either mass slaughter or Hippie Free Love d20. There's a whole swag of things you can do in between those; some of them involve combat, but most don't.
If we roleplay for challenges, well honestly resolving conflicts without smacking the other guy in the head is often more challenging than simply slotting him. It doesn't take much brains or creativity to say, "my character draws his sword." Figuring out other ways out of the situation takes a lot more creativity and imagination.
Sometimes we don't want to be bothered by that, and want the vicarious release that roleplayed combat brings, and that's fair enough. But sometimes we'd like to try something else.
So in summary, sometimes we avoid combat because it takes creativity and challenges us. Sometimes we avoid combat because it's fun.