It's true that if you signed a contract for X lessons and paid, and the contract doesn't specify the teacher, you can't insist on that teacher.
But bear in mind, you are also under no obligation to renew when your lessons run out. So you can
(a) tell the manager or business owner that if you are assigned "B" instead of "A" you will not renew and
(b) if you have flexibility in your schedule, say that you will change times to get "A" when they are available.
Mind you, the studio may be assigning you to "B" because they actually are better for you. Or not. They may be assigning you "B" in a bait and switch. Still, if you previously trusted the studio, and are kinda-sort stuck i this contract anyway, it's worth testing out the studio's choice for a lesson or two. But if the business owner ultimately does not assign you the teacher you prefer and who you think works for you, and the consequence is you don't think you are getting your money's worth, don't renew.
You can get more leverage if you inform them you will not renew if you don't get what you want. But given the contract, they still might not give it to you. If you are unhappy, change studios.