You have 2 jobs: teaching and being an entrepreneur
Being a teacher is one job. But being an independent teacher means you actually have two jobs. The "independent" bit means that you are an entrepreneur, which is another job, and so to succeed you'll have to do a bit more than just teach. Class pricing, collecting money, marketing and promotions, passes and memberships, insurance, liability... this is all on your plate. But it's really not that difficult, especially when you have the right mindset!