The main reasons that teachers work illegally (on tourist visas) are
1) they don't possess the necessary qualifications to obtain a teacher's license
2) their school / institute can't get them a work permit / won't get them a work permit / don't know how to get them a work permit
3) they actually prefer to remain a 'free spirit' often juggling around freelance work and not tied down to one particular establishment.
Be warned though: teaching without a work permit can land you in serious trouble. Jail / fine / deportation - take your pick.