Among English teachers, the term "native speaker" is a touchy and ambiguous subject. Now that I am going to explain it, I will open a can of worms. However, I will do this: use the worms as bait and catch some big fish with them and fry them up for you. So here goes:
My definition of a native speaker is someone who learned English from birth in an English-speaking country. Then, of course, to make this person a competent teacher, he or she needs to have studied at the primary, secondary, and university level in English. That way, your teacher will ideally provide you with the grammar and vocabulary you need as a student. I fit this description.
Now that I have laid out my definition, I think the next step might be to tell you that you should only study with teachers who are native speakers. That, of course, is a good sales ploy, but I'm not looking to offer my services to anyone, I'm looking to offer my services to people who are convinced they want to study with me after the trial lesson. On the other hand, I truly believe that a native teacher is not always the best solution.
First of all, you have to ask yourself why you are learning English and what type of person you are. Are you looking just to pass a test? Do you just need to learn written English in order to read textbooks? Or are you planning to travel to a country where English is spoken as the native or official language? Just as people use different tools to build a house, so too should you look for specific teachers according to your needs and goals.
Here are some reasons I think you might only want a non-native speaker of English to teach you:
On the other hand, there are many situations where a native is ideal:
You want to pick up culture and colloquial language. I as a native speaker have a unique way of speaking, of greeting students, of words that I don't even realize I'm using. If you want to use that as a model, then your English will undoubtedly sound more native.
In any event, it's always good to shop around and compare your options so that you get the best experience for your money. It's for this very reason that I offer a Free Trial Lesson.