I think I heard something about how people that get a lot of expertise in one area like doctors, lawyers, programmers, tend to far overestimate their skills in unrelated things. Sounds like you and the OP fall into this logical trap.
Whether the teachers are good or have good resources or have a class too heterogeneous to teach effectively is a different matter. But people who assume they know so much more than the experts need a humility and reality check.
"Those that can work, work. Those that can't, teach."Parenting rights can be revoked if there is enough evidence of potential damage to be inflicted upon the subjected children. I think the same should go for a lot of other things. People should not be let to freely teach or heal or whatnot without some minimum qualification when stakes are high enough, even it it's about their own children. Not when an actual free and qualified alternative option is available. You think you know better for your children, but if your children get damaged it's the society that will support the consequences when they'll grow up. The freedom to inflict damage upon others has to be limited even when others are our own children.
At the end of the day you're placing your trust in someone. They are just going to teach your kids what they think is important. Are you not willing to have an opinion on whether they are choosing the right things to teach?