Martial arts philosophy does not promote violence. It does not encourage the deliberate damage that brawling or street fighting can inflict on a person. Bullies that seek those types of scenarios so that they can beat someone bloody are not martial artists. The sport of MMA, through development of cage fighting championships and other extreme fighting promotions, is just that – a sport. It is not a martial art.
The very use of the word “art” in “mixed martial arts” is often deemed offensive. That’s because a martial art is a comprehensive system of conditioning for the body and mind, with peace as the underlying focus. Self-defense is emphasized, and most practitioners join martial arts schools for the self-defense aspect first. In the arts, defending oneself against attack is allowed when no other option is possible. Therefore, serious training in physical techniques, studying the art’s philosophies, and considering how each person makes a positive impact on humanity are the mainstays of traditional martial arts disciplines. The “martial” refers to the combat/defense aspect, and “art” represents the underlying peaceful philosophy, and the beauty that results when both are joined together.
Many techniques and strategies in traditional martial arts are dangerous and powerful. They are supposed to be used in defense only. Through solid training and adherence to a code of honor, a “defense-only” mindset is what an honest martial arts instructor will encourage.
For an interesting opinion on reforming modern MMA, read David Mayeda's article, "Contextualizing MMA in a World of Violence".