Combat training doesn’t automatically purge someone’s insecurities. It does, however, provide them with a base to build up confidence in themselves that can be extended into other aspects of their life. Over time, their confidence in their ability to fight and the pride they have in the skills they’ve developed marginalizes the other insecurities.
Instead of saying “I’m worth nothing to no one”, they say “yeah, I may look like an ogre but look at what I’ve done. I can be my own person and be proud of that person”. For them in the beginning, this means that even if they don’t think they’re good for anything else, they still have that one thing that they know they can do.
This is one of those funny questions that actually comes back to women, particularly American women and Martial Arts. In our current society, women are raised to believe that the only value they have is in their looks and are taught the only way they know they look good is if someone else notices them. Their values become built entirely around what other people think of them and how other people are interpreting their looks and actions. Martial arts as a sport is self-involved, instead of looking at others, you’re forced to look at yourself and find something of value inside yourself if you want to succeed. I faced some serious problems with diagnosed clinical depression in high school and often felt like “I’m a horrible, terrible, no good, awful person who is useless to everybody” but even as my brain said all that the small martial artist portion responded “but at least I can do full splits, perform a perfect front kick over my head, and choke a full grown man out in fifteen seconds.”
The training’s not going to purge your character’s insecurities, but they will have some measure of confidence and faith in themselves, even when the rest of the world is trying to completely rip it away from them. Fighting is a tangible achievement, skill is achieved through years of hard work. We can’t just throw that under the bus.