The question would be better framed to ask what level of instruction non-natives should teach. I agree with Torusan that non-natives are qualified to teach beginner and low-intermediate levels. There is no point in working on accent reduction if you can't have a simple conversation yet. I see this reflected in university-level language instruction.
Indiana University's Summer Language Institute teaches 9 levels of Russian. The two first-level classes are taught by Americans. The second-level class is also, but there are required conversation hours with native-speakers. All the classes above level three are taught by Russians. Obviously, 50 years of teaching summer Russian has shown that serious students need native speakers.
A super short answer for you Gigi is, if I wanted to learn Tagalog, I would hire you. If I wanted to learn English, I would look for a native English speaker.
All the Spanish speakers I know in America, are native Spanish speakers. I do not speak with non-native speakers. Because, the cultural questions I ask the native Spanish speakers, are an element of the their language. They do not have to read a book, or click through Wiki, to answer my questions about their home town, or foods their family ate as a child.
Ciao...
Just because a person can speak English, it doesn't mean he/she can teach English. I think that it should be based on a person's qualification which is kinda iffy at times because "qualification" per se can mean so many things -- I think that even if you don't have a TESOL,CELTA or TEFL, as long as you have a bachelor's or master's then you should be credible enough to teach general English and some specialized Englisg courses. I started teaching without a TESOL certificate but students think I am an awesome teacher (wink) because I have an MBA and they feel that I could teach them business English (which of course I was able to) and I eventually obtained a TESOL certificate after a few months.
Might I add that I was born in the Philippines and I've been living in the US for about 9 years or so now. I'm married to an Irish guy and we have three kids who can't speak Tagalog (and I always yell at them in English whew -- holy mother). I speak both Filipino and English and people can't tell that I'm an immigrant because of my accent and because I normally incorporate slangs when I speak. I do think though that I have a slight accent when I don't feel like speaking properly -- it's never gonna go away but can easily be masked if I want to. I can change my accent to British and Indian too lol.
My point is, anyone can teach English as long as they are qualified period! :-)
Non-native teachers can be useful for teaching a foreign language to beginners, using the medium of the learner's own language. For example, I'm sure that a Filipino or Filipina student just starting English would appreciate being taught by Gigi, as she would be able to explain the basics of the language using Tagalog. But once the learner has reached, say, lower intermediate level, I can't see why any learner would choose a non-native teacher in preference to a native speaker of the target language.
I think it depends on the level of the student. If I were starting out in any language, it isn't as important because I'm learning grammar, structure and basic pronunciation. But if I'm already more advanced and I'm looking for finesse points and cultural subtleties, then yes, I would want to work with a native speaker from the specific country I'm interested in.