"Mixed martial arts for children is growing quickly in the United States with an estimated 3 million boys and girls participating, some as young as 5 years old, the Daily Mail reports.
Supporters say the sport encourages self-discipline and teaches children how to win and lose well. Sebastian Montalvo is a New York-based photographer who has toured the country documenting the sport. Among his images is a photo of Kristopher "The Arm Collector" Arrey on his back, holding another contestant in a choke hold. Both boys are 7. The other child is crying.
While the referee asked the crying child whether he wanted to continue, the boy's father urged him to stay in the cage, Montalvo told CNN.
Although parents can get "mega-competitive," Montalvo said, they say the sport teaches courage and good sportsmanship:

"After every match, the kids are supposed to shake hands . . . One father started screaming at his son because he didn't want to shake hands after he lost. (He said) 'You go and suck it up and do it!' ". The boys shook hands."

Parents want to enroll children in classes of mixed martial arts for an important reason: the education of the children of their way to defend himself against the attackers and harassers
Some martial arts like Kung Fu take years to teach children the movements defensive or offensive unlike mixed martial arts, which teach children well catered bold practical ways to defend themselves.

Martial arts lessons give the child self-confidence and the ability to defend himself as gives him the courage to face the challenges of fighting battles in the street or inside a cage fighting.

"Critics call the sport barbaric and told the Daily Mail they fear for the safety of the participants. Some children wear no headgear and the gloves encasing their fists provide as little as an inch of padding.
While it's great to teach children to defend themselves, proper self-defense courses teach de-escalation and escape techniques to use to avoid throwing punches, Kiri Blakely wrote on Cafe Mom. She added:

Putting kids in cages and telling them to go at each other is no more than a fight club with children. It teaches them violence, not how to avoid it or escape it. If anything, teaching kids that they can win with a physical assault puts them in an overly-confident state of mind . . . ."

I agree with this speech somehow but lets do a little search about the best instructors, be careful of what classes your children will reach it.
Children must have special course especially at the beginning of their learning period to know how to fight and how to escape, what is the danger in doing some movement, what is the best way to do a fighting technique,... etc.

MMA should not aim of randomness of fighting techniques but you must know MMA programs include at least two fighting arts, i.e a program include grappling with boxing and/or taekowndo with grappling, so that it is called Mixed martial arts.

Locations of Martial arts classes in USA:
chicago MMA classes
What is the best Martial arts for my kids?