As is obvious, I'm a huge proponent of martial arts for people from any age (especially for kids, but I'll write this in general.) And not just for the typical "discipline" reasons that most people propose (though that's one big reason.) There's a litany of reasons, so therefore in the spirit of the Internet, I'm going to write them out in a list. Because the Internet loves lists. Note that these reasons aren't in order of "most important to least important," and everyone's priorities for it can be different. It's also not all inclusive. But whatever, here's some of the many benefits:
1. It teaches that pain can be overcome
While a good martial arts instructor will know the cues for actual, legitimate injuries and strop training when necessary, learning how to manage pain is a huge benefit of martial arts training. Learning that physical and mental pain doesn't have to stand in the way of your goals is incredibly useful. Being able to push past your physical and mental limits in spite of agony brings a sense of context in all of your other endeavors. Plus, coping with pain is a great way to learn about your body and its limits in general.
This, by the way, is especially true in a full-contact martial art. I know it can be worrisome to some to imagine getting hit, but the human body is remarkably resilient, and with training you actually learn how to mitigate damage better.
2. It teaches confidence and inner strength
This is one of those stereotypical benefits to a martial art, but it remains true. Good training in martial arts provides people with a sense of self and confidence that will benefit them later in life. From the obvious sense of growth (which is another point) to learning how to overcome barriers (which I mentioned above), martial arts can give people a chance to know that applying themselves can yield positive results. It's important to note that confidence and arrogance are different, and learning to differentiate between the two is also something that is often learned in training. Being confident that you can overcome a challenge is not the same as believing that you're always going to be the best regardless of what you do, which brings us to...
3. It teaches how to accept losing
Sometimes, the best lesson in life is the hardest one where you are the loser. Martial arts will teach you how to lose, guaranteed. Learning how to accept losing and learn from it is one of the greatest skills anyone can learn. It teaches humility and confidence at the same time, because it teaches people how to grow from the position where they lost and to move past it. Sometimes, it's literally being kicked down. But learning the strength to get back up and keep going is something that everyone can benefit from in their lives.
Plus, you learn very quickly that there is always someone better. Which brings up...
4. It teaches that there's always someone better, stronger, faster, smarter, harder working...
Even if you're pretty good, there's always someone better, stronger, etc. Learning this and learning from it is a great experience because it gives you people to look up to, and it gives you reasons to work harder. Learning how to discover someone who's way better at something you work hard at is a good experience because it teaches you to cope with the feeling of being inferior.
5. It's a really good workout
True story: my first class was so hard that about 3/4 of the way through, I almost gave up and left even after paying for my gi and membership. I couldn't believe that anyone could work that hard. I left the class sweating, panting, and thinking to myself, "this is nuts!" I literally hobbled up the stairs to my apartment, and drew a bath of lava and stayed in it for about 30 minutes.
Then I went back, and it was a little easier. Then I progressed a bit more. And so on. Now, even though I sometimes get tired and slow down, I'm usually the one cheering on other people to keep going. I've learned to push past my limits, to breathe better, to use my body more efficiently, and I've improved my physique beyond anything I've known in my life.
Moving the human body is really hard for the human body. Most of us are not used to pushing ourselves to our limits (no lions chasing us around, maybe?), and we don't realize just how hard we can push ourselves. Training hard will teach you your limits, how to break them, and how to view them as temporary impediments.
6. You meet the most interesting people
It might sound a bit odd that a sport where you perform violence on one another makes you great friends, but I've met some of the best people in my life while at events and competing. I've been fortunate to meet people from all around the world, including every continent. Even in your own dojo/gym, you will train and become friends with people of all walks of life. My group includes students, lawyers, doctors (my wife included, hah), an auto mechanic, an engineer, and even a PhD chemist. Everyone brings experiences, thoughts, beliefs, and training to the group. From the newest student to the experienced fighter, everyone brings something to the table. The best part? They're all constantly growing and learning with you, so you all have something new and interesting to share with each other on a constant basis.