Introduction: I teach students how to understand music in all facets. The only way to do that is to treat it like a language. Music has an alphabet, and words, and sentences just like all other languages. That means that I focus on listening skills first, before reading. Learning to read music, without understanding what it means, would be like memorizing a speech in Russian without understanding its contents. Music theory is an essential part of performing music of all levels.
I can't tell you how many times I've met people who quit playing piano because they just kept having trouble reading music. Little did they know that with a little understanding of chords and melody, they could play most of their favorite songs, without reading any music at all. I can't tell you how much money I saved just reading chord charts, rather than spend $100s on different sheet music books of the latest songs, most of which aren't that great anyway.
That's not to say reading isn't important, but you can't communicate in the language of music until you understand it. I love showing people what is common to all the music we hear. Armed with knowledge, any popular song isn't something you learn reading music in a week, but rather something you learn looking up chords in an hour.