Let me briefly tell you my personal story with music as a hobbyist. 

TLDR : Got taught technique as a child, had no fun and quit, learned music by ear by myself later in life, having fun now and playing. I don't get why music is taught the way it is.

Retrospectively I wouldn't teach myself the way I was taught. I know plenty of people that had the same kind of disappointing learning experiences in music schools and have since stopped music.

I really feel music school are turning a vast majority of kids into music boxes at best, instead of making them musicians. 

Why are music schools teaching the way they teach ? 
Where should I send my kids for them to learn music ?

The longer version : 

The farthest back I remember was making noise on my own with some electronic organ when I was 5 but I still remember I could spend hours pushing various buttons, switching instruments, pressing keys, and having fun doing so. 

A few years later, my parents, having noticed my interest for music, started me off in music school; for the first two years it was just music theory. Then around 9, I started the piano. It was playing by the sheets, and learning scales. Basically learning the technique. I remember that I always had a rhythmic problem, always giving myself the liberty of stretching times to make it sound the way I preferred. 

But every time I was corrected and made to play on rhythm. After a few years of that I became correct at playing mechanically, playing the right note on the right time. But the fun was going away at the same time. It was no longer about making the right sound or melody but more getting the right finger on the right key. 

I also remember that when I learned to play a piece at most I had listen to the whole piece one or two times. I had a few teachers but it was always the same policy.

At 16, I stopped playing. 

Ten years later, I tried to start playing again on my own to get stress out during a difficult life period. I began by following the same recipe I was taught. But quickly I realized it still was no fun. 

So I decided to learn it my way. I wanted the music to come naturally. 
The first month was just forcing myself to unlearn the mere fact that when I was pressing for example the "C key," my brain was saying "C" to itself. I played by making simple patterns of sound, and repeating them randomly at first. Then trying to search for patterns. I tried to make my own rules I would try to follow. And at all times I tried to listen to the sound the piano made while I played. In short I was exploring music on my own.

Over the course of a few months, playing half an hour a day, in a sense, I quickly picked harmony, rhythm, transposition, a sense of understanding and feeling. Sometimes I listen to a song and try to replay it. I try to get the theme, modify it a little on the fly to see where it takes me. 
After two years of my own learning, everyday I'm still picking up new things; it is fun, varied and interesting. 

I am still very far from being expert, and I've still a lot of problems if I try to play a music by the sheet, but I'm happy creating a simpler variation to make it less technical if I think I get the main idea right. I still don't get the fun of making things technical for the sake of being technical. Even though I can get pretty technical in my own compositions. But sometimes I feel I rediscover some technique tricks. And I've no doubts that in time missing techniques will come naturally to serve the need of expressing ideas.

Now everything I was taught over my years in music school make sense to me but it seems like it all was presented backwards.

I can see that all that was taught has some value, but if I had not restarted from scratch I still would not have gotten it. 

I feel that presented the way it was, I had no chance at all of picking it up. I even feel that I would have picked it up if the teacher was not constantly depriving me of any liberty I granted myself. 

Why do music schools teach the way they do?