The most important thing you should consider is the person's capacity, and never where he or she is from. Being a native speaker doesn't mean you know the language well enough to teach, it doesn't even mean you can teach. As a pedagogical coordinator for language schools, I make EVERYONE applying for the job take an English exam, and surprise: a lot of native speakers of English cannot pass an English exam.
That's funny because in almost all schools, only non-native teachers have to go through a difficult English exam, that is, if they even have a chance to get the job, because many schools have the policy of hiring native speakers only. According to the law in the European Union, that is job discrimination. https://teflequityadvocates.com/2014/04/01/native-speakers-only-ads-and-eu-law/
Linguists agree that native and non-native speakers can be equally good teachers. They go even further and say that considering native speakers the ideal language teachers is a fallacy. https://teflequityadvocates.com/2014/07/06/interview-with-david-crystal/
But if that's so, why does the market prefer to hire native speakers? Rather than a pedagogical strategy, that is a marketing strategy. It's a way to pay less to the employee (who many times is just a native speaker without qualification) and charge more from the student by advertising: STUDY WITH NATIVE SPEAKERS. I've been inside this business, and when schools are not serious, that's how it works.
- Methodology and way of working.
When selecting your teacher, these are much more important things you should consider than where he/she is from.
Hope I've helped you get more food for thought! :)
My mum decided to learn English and she's a beginner from scratch and we tried qualified native speakers to teach her and it was a total failure. First, apparently native english teachers tend to think that beginners do know some English because they would try to speak English to my mum and back then she couldn't even reply to questions like "How are you?" but of course we read their profiles beforehand and they assured that they're experienced with beginners. So we decided to work with a Brazilian teacher that teaches English and it has been really helpful. So, yes, sometimes a non-native teacher is the best option depending on your goals, if you're a beginner, if you're the type of person that needs comparison between the two languages so you'll be given logical explanations (a lot of people can't simply adapt to the natural way of learning or learning by doing).