I missed all the grammar classes in middle school because GT classes replaced the English classes and for whatever reason the school did not think we need to get grammar instructions. As a result, I would not be able to teach gramar without some kind of resource because I actually don't know a lot of the terms. I don't really know the rules but mostly I write by feel/sound.
That, in a nutshell, is exactly why it should be taught. Someone who doesn't learn the lingo can't teach it to someone else. If a teacher makes an editing mistake, the student can't articulate why they had it right. Etc.
Also, it's pretty easy to fall into bad habits, and knowing the rules makes them easy to correct. For example... sometimes I'm guilty of abusing ellipses... they look kinda cool... and they convey what I'm trying to say in the manner I'm attempting to say it... but once it gets out of control, I can look back and see where I'd be just as well served with commas and periods.
