Nearly always! Human evolution is the story of avoiding conflict. Humans had two million years of cultures which minimised ego and minimised violence. (The idea of humans as inherently violent is only a creation of civilisation.) This was often done through avoidance, mediation and humour.
Look, if you can avoid a fight, that's your best choice. Even if you're big and muscular, fighting always carries huge risks. All it takes is one misstep from you, or a lucky strike from the other person, and you could end up seriously wounded, or dead. Often we overestimate our strength, or underestimate our opponent, and then are shocked (and injured) by the result. You just never know.
A basic rule of self-defense is, if someone threatens you and you have the opportunity to escape, then escape. Run. If someone threatens you with a knife or gun and asks for your wallet and jewelry, give it to them, and let them go away with what they want. It's not worth risking your life for money or jewelry.
On the other hand, if it's clear someone intends to hurt you, then you MUST fight back.
When encountering wild animals, you take the same approach. Slowly back away from the grizzly bear, or elephant, or mountain lion, snake, shark, etc. Wild animals aren't usually interested in humans and don't normally go looking for a fight. Fight back only if attacked, and then, do it with everything you've got.
The bottom line is, in fights all parties involved usually suffer injuries, even the “victor”. Look at any war. Every side in a war suffers, especially the general population, and of course, the natural environment. So really, no one wins in any war. Sometimes, both sides are absolutely guaranteed to suffer immensely. The perfect example of this is nuclear war. There is no such thing as “winning” a nuclear war. In a nuclear war, everyone on the planet loses. This has been called "mutually assured destruction" - MAD. (Anyone growing up during the Cold War, from Russia and the U.S., especially, would remember this.)
Even in fights between two people, whether physical or verbal/emotional, no one really wins. There are always emotional and psychological costs. Sometimes worse. It is a pyrrhic victory; that is, the price paid for any perceived "victory" is actually so great that it adds up to defeat.
Which underscores the important idea: if a fight isn't necessary, then avoid it, because things could get a whole lot worse for you. Put aside your ego, count your blessings, and get on with your life.
As the military computer Joshua in the 1983 film Wargames says;
"The only winning move is not to play."
For more on peaceful cultures, read these books by Douglas Fry: