It is a truth universally acknowledged that when a man is in possession of an arrogant disposition and a gloating tongue that he must be in want of attention.
In plain English, no one likes a braggart. You know it, I know it. When was the last time you actually enjoyed listening to someone talk about how amazing they are? Conceited people aren't interesting or engaging with anyone other than themselves. The occasional obligatory "stroking of the ego" and "tooting of one's own horn" is all well and good and healthy (and oftentimes enjoyable) but when your achievements/skills/exploits become the centerpiece of your conversation, it's time shrink your head down to a manageable size again.
Modesty, a benefit of martial arts training, is a foundational pillar to becoming an elite leader, powerful black belt, and just an all-around pleasant person. The ability to objectively view one's accomplishments and be able to downplay (but not deny) their prowess is a skill that ought to be more openly admired and respected. When practicing modesty, one may notice a distinct difference in how others treat you. Suddenly, instead of having to compliment yourself, others may grace you with a kind word or two. People may have more interest in what you have to say, and will find your company much more agreeable.
Arrogance only breeds disdain. Modesty, on the other hand, leads to more opportunities. A humble attitude and politeness go hand-in-hand, and the last time I checked, good etiquette led to some nice returns. Better relationships, more interesting conversations, and more chances at opportunities not offered normally to people, to name a few. Looking at it that way, why wouldn't you want to gain a more humble outlook on yourself? It's not particularly difficult, and you'll come out better for it. In the end, only good can come of attaining a strong sense of humility, and implementing it in your daily life.