Yes, mixed martial arts encourages domestic violence and assaults, because a person cannot watch that must violence for that much time without becoming violent themselves. If a person watches television in French all day, eventually they will start to speak French. If a person watches violence all day, they can't help but start to rationalize that type of behavior.
Martial arts is both an art and a dicipline. Bottom line it was created for combat before it it became a sport. It should be treated as such with responsibility from those who practice it.
It should not be in such irresponsible hands that encourage irresponsible people to practice it or flaunt it. That in itself encourages irresponsible behavior to others practioners or not.
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Martial arts teaches you how to humanely disable an attacker without causing life long harm. My teachers even tell me that the one thing you never do is slam someone's head into the ground because you could hurt them. We are not violent people, and we are not being taught violent thoughts. We are learning how to defend ourselves, and live by a moral code that says "I will not harm any living being" and "I will not use my skills for violence"
Just like everything else domestic violence is a choice the person makes. I feel that Martial Arts tries to teach you calmness, respect and being responsible not just going around hitting people. Any one can make the choice to hit a woman whether they are martially arts trained or not.
Mixed Martial Arts is a sport, and those who cannot distinguish between sport and regular, every day situations have a psychological issue that needs to be addressed. Football players can't tackle people off the field, hockey players can't body check people on the street - The same applies to MMA. What happens in the ring is sport, what happens outside of it is assault.
I think that the concept that martial arts encourages domestic violence is ludicrous. It is like all things in this life. It can be corrupted by people who choose to do such things. Like guns for example. Most people have a gun for protection from bad people who want to do harm to them or their family. Then you have those who use them to cause harm. It is all in the person who uses it. I think it is supposed to be used for protection not to wreak havoc.