We don’t teach reading. We teach children. Or should do anyway.
That's a bit of a quibble, isn't it? After all, we teach French, English, geography, maths, physics etc. Mostly to children, but adults can be taught all of these, and reading, too.
As I understand it, ITA was made learning to read very easy because it taught only one symbol per sound. Many languages have a similar structure to their written words, one symbol per sound, but English is an amalgam of many different languages, each with their own system of representing sounds with a letter or group of letters.
The problem with ITA, of course, was the one that those who adopted it didn't give serious consideration to, the conversion from the ITA to the conventional alphabet. Mind boggling when you think about it 
It wasn't the only 'fashion' in the teaching of reading that was unevidenced and damaging to many children...