Avoiding a foreing accent when speaking?

منذ ٥ أعوام

In my journey of learning a different language I have come across many different teachers. Some of them used to focus a lot on avoiding having an accent when speaking and therefore sounding more "natural".

Personally, I prefer not to teach "avoiding" an accent when speaking. What do you all think on this? 
Any thoughts on where this tendency to sound exactly as a native speaker came from?

I would love to hear your thoughts on this!