Students these days tend to really care their English teacher's pronunciation. They seem to believe that English teachers should pronounce just like a native speakers of English. What do you think about this belief? How would you react to this attitude (belief)?

I disagree with this idea.

The pronunciation is important in teaching because students are following what teachers do. If teachers pronounce English with wrong accents, there are high chance that students would imitate teachers' pronunciation. When students are more familiar with wrong pronunciation, they would have hard time fixing their pronunciation to the correct one. Therefore, it is important that teachers pronounce English like a native speakers of English.

However, in some way pronunciation is not that important if teachers are using listening materials. Pronunciation problem can be solved by teaching students with listening materials. After teachers teach students correct pronunciation, there will be no problem about teachers being role model of speaking to the students. It means that if teachers already taught students correct pronunciation with listening material, then students won't  confuse and make  same mistakes as teachers.

There are more important matters in teaching English to the students like grammar.  Being able to pronounce correctly is just additional ability to become a good english teacher. Without correct pronunciation, English teachers can teach students correct English. So I don't believe that English teachers should pronounce just like a native speakers of English.