Even in Buenos Aires, a place of highest tango dancing level, where there are many famous and excellent teachers; many unknown yet still excellent teachers. There are plenty of pretenders.
To a student, like me, a good teacher has to have the following criteria, specific to teaching tango (the dance) but applies for all fields of instruction.
1. Knows tango inside out:
Well versed in the theory behind tango and from different angles. So he would be able explain clearly and more importantly anticipate different problems faced by the students.
2. Has a lot of social dancing experience:
Argentine tango is a social dance, you want to teach students who would eventually be dancing socially, you better have a lot of practical experience. Because some things can only be learnt by dancing socially. Navigation of the dancefloor, musicality, how to adjust to different followers, etc.
3. Knows his students:
He must have a keen eye to judge the students' dancing level and also learning capacity. Only be this way he will be able to teach the appropriate material, at the appropriate pace.
4. Able to communicate effectively:
After having a solid foundation in tango, knowing your students, the next thing to have is to able to transmit this knowledge to them. To bring about your points clearly, that would be dependant on your own communication skills. Also to have a clear and planned cirriculum and also class structure. That way the students can learn things step by step.
5. Recognize that tango is an more an art than science:
There's is no one true and universal way to walk, no one true and universal way to embrace. No one true and universal way to dance. Its an art. It is unique to each and everyone. This is difficult because a balance must be struck to ensure uniformity in instructions but also allow flexibility for each individual. At the end of the day, even explaining the same concept needs differing explanations to different people.
6. Have genuine passion and care for students:
Above all, if the teacher has this genuine care to nuture the best out of his students, everything else would follow.
To sum up, know the subject well and be able to pass it down.
So its not easy to be a teacher. Even harder to find a good teacher. Pretenders however, are abound.
From my own personal tango journey, taking classes from various teachers. These are things I've encountered from pretenders. These are the consequences of their actions (besides sucking money from us) which I experienced personally or from other students.
1. Lack of knowledge; People who have no clue what they are teaching.
Personal experience: Teacher putting on a 'milonga' music when asking her students to practise 'tango'.
2. Lack of social dancing experience; People who are teaching figures not suitable for social dancing.
Personal experience: Granted you have some students who are looking to stand on the big stage one day and perform. Most tango students are looking just to enjoy the embrace and the music. As a consequence of their teaching, you have people getting hurt in milongas from big back steps, crazy boleos (flying kicks) and secadas (more flying kicks).
3. Lack of judgement of students' level, People teaching way above students level.
Personal experience: Instead of learning things in a comfortable pace, no learning takes place due to everyone struggling for their dear lives and balance just to do that crazy step. Eventually when the students finally does something that looks like what was being taught, it is with super bad posture, bad balance and of course 30minutes after the class ends, they will never be able to do it again. I personally have hurt a fellow dancer trying to practise back secada on her, just after 2 months of dancing. I blame both myself and the teacher who taught it.
4. Lack of ability to communicate effectively.
The strange thing is I have no problem in this area. All the classes I attended so far are in a language I can't understand. 
But I'm doing ok haha. But there are some teachers who arrive in the class, spends 30 seconds thinking of a figure on the spot and starts to teach it.
5. Rigid in style.
I understand some teachers have the mentality of if you want to attend my lessons, then you must learn my style. And no qualms with that. Its a free world. But to beginners who don't know the existence of many other styles, or not aware of the personalization of tango, they would become as dogmatic as the teachers and as a result be stuck in a small world of their own.
6. Lack of real passion and concern for the students; Some just want your money and in Buenos Aires, many are just riding on their fame.
Personal experience: Teacher demonstrates a complex figure 3 times and goes out for 15 mins ciggaratte break.
In Buenos Aires its not easy to tell the difference. But fortunately I have a sufficiently solid foundation given by my very good teachers (Royce and Jean Michel) back in Singapore, to distinguish from the teachers and the pretenders.
I'm still in the process of trying out different teachers. Some I like instantly, others I had to walk out in the middle of the class. Hopefully I will be able to come out with a short review in the future, for the benefit of whoever is interested.
