I believe it would probably be best for me firstly to describe first exactly what 'mix martial arts' is and then go into a bit of its history before I start discussing why getting kids involved into mix martial arts could be beneficial for them on numerous levels.
Mixed martial arts which is more commonly referred to its abbreviation of MMA is considered a combat sport, such as with most other martial arts, the main difference is that mix martial arts incorporates a range of these combat techniques and style such as from Boxing to Karate, from grappling to kicking. Where as usually one specific martial art will have a certain style of doing things (e.g. Judo focuses mainly on grappling), MMA on the other hand allows you to 'mix it up' almost creating a unique style to every fighter, that compliments their strengths.
It probably won't surprise you, that it originated from certain styles claiming that theirs was better than other styles, and the rules implemented (not that there were many in the early days) would find out which style was truly the most effective. Then it was only later did fighters start to incorporate multiple styles into their own personal unique fighting style (along with many additional rules to increase the safety of the contests).
How Mix Martial Arts Will Benefit Kids?
Mix martial arts will help your kids on many levels, here I will briefly just go over a few of them but for more I suggest you check out:
Exercise - probably the most obvious factor, is that by participating in mixed martial arts classes for kids, your child will be developing a healthy and strong body as mix martial arts is keeping them fit and active by participating in classes and practicing at home. It will also improve secondary physical skills such as concentration, hand to eye co-ordination, balance, flexibility, control of fluid movement etc.
Social - at an early stage it is important for them to develop their self confidence, interpersonal skills and social ability, and these mixed martial arts classes will provide a great platform do exactly this, by being encouraged to work together to develop their ability further. Whilst also attending performance events where they will carry out demonstrations at events. I found that there was a lot of positive role models to follow in my class and I believe that I have copied many of their good habits to this day.
Discipline - personally I think this is the most important factor I took away from my classes in martial arts, it teaches you about respect. Respect for your fellow students, respect for your teacher/instructor, and provides a channel for your child to release frustration in a positive manner. Which will reflect in all aspects of their lives through to respect for school and home life too. I know personally it has been a very positive experience for kids with troubles from the bullied to the actual bullies.
Self Defense - another rather obvious point is that your child even from early on will be taught how to deal with potential physical conflict and keep themselves safe. However, it doesn't just teach them to defend themselves physically but also psychologically, when facing a bully (who is most likely to suffer from low self esteem and picks on others to feel more powerful) a mix martial art student will have been taught to subconsciously show no weakness and look their opponent straight in the eye, respond to verbal insults with a firm voice, and propose a confident posture, all of which contributes to putting a bully off picking on this student as a victim and this is what in some classes is described to as the art of 'fighting without fighting'.
Still Unsure About Your Kids Starting Mix Martial Arts?
From what I have said above I wouldn't be surprised that if you are a parent or guardian you maybe rather sceptical and reluctant for your child to join due to being afraid of your child likely end up getting in some way from what seems to be a rather violent sport.
This however is a rather problematic misconception, especially in the case for children. As it only is really considered a dangerous combat sport when you are in a competition, where as with sparring and practice often their is fairly minimal contact and is done a safe and very strict manner (e.g. heavy body and floor padding, and with an experienced instructor etc.), if you compare it to sports such as football and soccer there is probably just as much risk if not more for your child getting hurt in these sports as well.
If you are still unsure I would encourage you to read more around mix martial arts for kids online or even get reading into some books such as Mixed Martial Arts for Dummies which will show you more options on how your child can get involved in local clubs, what kind of age of your kid should be joining mix martial arts classes and so on.