Linguistics

You teach the currently relevant rules, vocabulary and literature while the students learn the rest through cultural osmosis. Like every one of us did.

Because you have to know the rules and conventions to be able to break them effectively - if you don't know that "theirself" is not grammatically correct, then your sentence reads as sincere rather than sarcastic

I would argue the main benefits are to teach people how to effectively switch registers as the context demands, and to expose them to a range of language they likely wouldn't ordinarily encounter in their daily lives. English teachers could do to lose the judgmental aspect of "This is the one true way to speak English, the way you talk amongst yourselves is wrong and you need do stop," but there's a definite value in teaching students, "This is a way to write/speak clearly and effectively that will be understood by quite nearly every other educated English speaker you might encounter."

As far as exposure to a broader range of language than one normally encounters in their life, I saw the importance of this first hand with many of my coworkers who were heritage speakers of Spanish. It's not my native language, but it was my primary work language for a good 5 years, and I wound up getting put on interpretation duties for our safety meetings over a native speaker with pretty limited formal education in Spanish. For topics to do with daily life, family, friends, etc, this guy would be able to speak much more naturally than I could. I might not say something that was exactly wrong, but perhaps I would be too formal or make odd word choices he wouldn't. The problem was, he completely lacked any technical and professional vocabulary, and had no concept of what words/phrases were unique to his own country and what alternatives might be more widely understood.

We would have safety meetings once a night, and they would have topics like, "When a forklift has its forks in the air, don't walk beneath it, as hydraulic failure could lead to injury or death.". He translated that one night as "Cuando la vaina del pasillo tiene esa vaina de en frente en el aire, no pasen por debajo de la vaina. Es peligroso." Basically "When the thing in the hall has the thing in front in the air, don't walk under the thing. It's dangerous." Best case, he might say "El forlift," but he would never land on "el montacargas," or even think to look it up. Some of his wilder attempts at interpretation didn't work for anyone, and the ones where he just used a Spanglish version of technical terms only worked for other coworkers who already knew at least a bit of English, and probably didn't really need the translation that much to begin with. Unfortunately, we had a fair number of employees who were monolingual Spanish speakers that he found himself just completely unable to communicate with effectively.

Granted, not everyone takes full advantage of it, but English classes do (or at least should) expose you to a broad range of the language, as it's used in various contexts and forms, while also furnishing students with the ability to expand upon that and adapt to new contexts on their own in the future. Failure to do so leaves students with stunted linguistic and communicative abilities.

are you asking why english should be taught in non-english native countries, or in anglophone countries? Because the former should hopefully be obvious, being able to understand and use english is pretty useful these days..

The latter, teaching languages to people who already know them, is something i'm more iffy about.
I think it's dumb to make it mandatory, instead we should have optional general linguistics courses and encourage people to read.

Maybe as part of history class you can learn about how your native language was spoken in the past, as well!

Most people are not that creative.