By the time I was 10, I had been playing classical piano for five years. That means, at the age of 10, I knew:
1. How to read music very well (couldn't quite sightread yet, but close).
2. How to rattle off all the sharps and flats in various key signatures, without any effort.
3. How to play major, harmonic minor, and melodic minor scales in 12 different key signatures, four octaves up and down.
4. How to play Bach and Mozart and could identify some things that made them uniquely who they are.
5. How to keep two or more distinct melodies going on at the same time.
This is all simple stuff for a classical background, and all this despite never studying anything beyond just playing the music in front of me. I would never say that piano is the best instrument in the world because I prefer guitar, after all. However, I gained all this theoretical knowledge despite never studying it... because that's all classical piano is. Just in the process of learning how to play the music in front of you, you become theoretically proficient. Can't really say that about guitar because I know many dudes who've been playing dozens of years, and how many of them can tell you that B major has five sharps?
That's why I'm going to give my kids piano lessons and they can pick up guitar when they're 12.