I think a lot of teachers may take the view that grammar is not essentially the best place to start when learning a language as this can confuse new learners. I feel the best place to start is by learning the sounds, spelling and pronunciation of a language and then moving onto basic vocabulary. More often than not grammar is learnt subconsciously anyway due to the culmination in the ​time of grappling with a language and its structures.

In order to teach grammar you don't only have to be a native speaker but also you should be able to explain the language to non native speakers. Let's take your first language for example. You have spoken it since birth ,you use it in your daily life situations. So if a foreigner asked you why you say it this way? The normal answer would be " i don't know. We just use it like that" that's why you have to take courses in teaching the language for foreigners cuz you will find tons of weird questions being addressed to you. That's why you should learn grammar from a native speaker with a certificate for teaching the language to a non native speaker and not only any native speaker. And, Grammar is definitely important. How will you build up a sentence without using grammar?

I have not taught every part of English grammar but I am sure that every part can be taught in some way or another. I cannot imagine how adult students can understand advanced grammar simply from speaking and listening. On the other hand, many students are good at studying grammar but are not fluent because they are not able to spend enough time speaking and listening.

Grammar is important (there is a difference between 'I went' and 'I will go'). But it shouldn't be taught in a traditional way when you study rules and try to apply them in different exercises. I find it better to introduce it in a natural way so students don't know when they learn it. Later I explain them some basic rules.

It may be that the teachers simply do not know the grammar! As a native speaker, you often don't learn any grammar - the first time I ever learnt any grammar was when I learnt a second language. You can certainly learn a language without grammar - after all, that is how we all learn our native language - by absorbing it. But grammar does make it easier to learn, and how important it is depends a lot on how an individual learns. Some people learn better by absorbing, some by remembering rules. Having both available is obvious best to cover both styles. It is also important not to overstress the importance of grammar, particularly in a language like English, which is so irregular, and more importantly, that is not defined by its grammar. Grammar is just a description and interpretation of the way people write and talk.