I have been teaching English in China for just over 6 years. However, I don’t teach English. Very little of my class time is spent on grammar. Punctuation and spelling don’t play big either. All of these things can be taught just as well, if not better, by a native Chinese teacher of English. They have studied the grammar books and can explain the technicalities of the language to the students in a way they will understand.
Instead, what I teach is culture, geography, lifestyle and history. Through this, I create an understanding of the language and how to use the language that a non-native speaker cannot match. Of course, an American will teach a slightly different set of culture from an English person, so a student should seek to study with a variety of teachers from different English-speaking nations.
Though non-native English teacher may have a good English skill, they don’t have the same knowledge of the culture of England or America. They have their own nation’s culture. To many employers, this nation’s culture will seem to be not relevant to English study but more relevant to a study of that nation’s language.
Aside from this, there may be issues of racism and preconceptions about what makes a good teacher. There may be ideas held by schools or parents that English teachers are white Caucasians or that teachers have a certain accent. Should you differ from these preconceptions, you may find your employment limited. The opposite may also sometimes be true. Some people who look right might find offers of teaching jobs even though their own English skills are substandard.
This is not to say those non-native teachers cannot teach English in China. They can and they do. I know Iraqi, Bulgarian, French, Nigerian and South African teachers working here, whose native language was not English.