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Unless you can provide other useful services to help the teacher to manage thier students. Maybe scheduling, accounting, payments.

^ Exactly - this where 'commoditizing your complement' comes into play: https://www.gwern.net/Complement

In that case it seems a lot easier to skip building a marketplace and just create booking software for music teachers.

Though you'd probably find that most were happy with Google Calendar, Xero and PayPal / Square.