Minors are not allowed to sign contracts for a good reason! A small child really does not understand the long-term implications of a request like this.
My mom signed me up for slide guitar, at my request, when I was about 10. The salesman's guitar sounded so very cool! I discovered by the end of the first class that I couldn't bear the sound of all those beginners on all those cheap student instruments. It made my nerves ache and I felt desperate to get out of the room. (I've since learned that I have sensory issues, but that term wasn't around when I was young.)
My mom wasn't rich, and she forced me to complete most of the classes she paid for. After a few weeks, I would get the most terrible stomachaches when I even tried to practice. But she'd "spent all that money" on me, and didn't want me to duck out on my "responsibilities and obligations."
It's taken most of my last 40 years to learn to love and appreciate all that my mother did for me, because her many ideas about what "should" be were so badly misaligned with what actually "was" for me. And her lack of respect for my authentic needs resulted in my not being able to respect my own very real needs. Not healthy, and not something we consciously would ever wish on our beloved children.
Based on my experience, I would be inclined to honor my child's preferences when they are stated so clearly. He may have asked for the classes, but the money is YOUR issue, not his – it will be at least 2-3 more years before it becomes meaningful to him. Not his fault: he's simple not conceptually ready to grasp what it represents in terms of value or the difficulty of earning it.
Demanding he never quit something he started could backfire someday – what if he starts an activity, a dare, or a relationship dangerous to his physical or emotional health? Forcing him into an activity that "should" be fun for him will not make it so. It might simply make him resist more desperately. As he gets older, if your demands make no sense to him in terms of his own needs, he may become more defiant, or he may give up emotionally to please you. Either outcome is tragic.
What he does know, intimately, is what his interests and fears are. Have you talked to him about what he wants (or does not want), and why? What do you believe about parenting that makes it so important that he does NOT "get his way?" Does that mean EVER? Is that something you are carrying from your own childhood? Is there a more flexible way to look at it? Do you want him to learn all the lessons, or are there good lessons in this situation for you to learn, too?
I hope you'll consider cutting this little guy some slack, M.. Firm parenting is important, but compassionate parenting can be firm. And it can make our kids' eyes sparkle.