Loads of musicians are self-taught.
The ease with which you leardn depends on the twin factors of desire to learn, coupled with basic ability. That's why some people can progress seriously easily, and others struggle for years and never get it.
I interviewed a delta blues player at a festival recently, he is fourteen, and his music teacher put him straight into Grade Four exam, wich he passed, then he did Grade Five, skipped Six and Seven, and passed Grade Eight.
Similarly, Cherisse Ossei who plays 'live' drums for Mika, was promised her kit of choice by her dad when she passed her Grade Eight, imagining she would have either given up, or be old enough to have left home by then! He had to honour his promise when she did pass - at the age of fiteen!
So, you can teach yourself and discover an inbuilt talent, but the essential part of learning any instrument is to have fun, so even if you only master Chopsticks, if it gives you pleasure, then that's really all you need.