I tend to listen to music when playing casually like in Normals. However, in ranked, I keep it off in order to avoid distractions and focus more on what's going on in-game.
Essentially, you are re-allocating your brain's resources in order to better play the game. Although some may be a bit more dependent on audio cues to react to situations, others, such as yourself, don't need sound as much. By cutting off the need for one of your five senses, your brain can focus even better on the visuals of the game and coordination with your hands.
Another reason could be irritation. Some people really hate hearing certain champion voices, like Yasuo's "Hasagi", Lulu's laugh, or just the sounds of the game in general. By not having to worry about this potential source of agitation, these people can play the game without such distractions.