Wow! You have a cheek taking money from students as "a professional English teacher" when you don't know the difference between the definite and indefinite article!

You are advertising yourself as a professional English teacher with English as your native language and you don't know even the basics of the English language?

'a' is an indefinite article so it means 'a gym' is one of many possible gyms it is not said which gym it could be. 'the' is a definite article it means 'the gym' is a specific gym probably the only known gym in town. The hearer usually understands which gym.

'the gym' is like 'the post office' or 'the bank' - any of them suffice for the purpose, and no one normally asks 'which one'. 'a gym' is like 'a restaurant' - a situation in which a choice is made between alternatives. :)

Maybe one of his students hacked his account