The main advantage of puppy classes is socialization. The next time he asks, tell him she learnt to listen to you while there are other dogs and people around. She learnt how to communicate with the other dogs. She learnt loads of social skills that will come in handy later. She learnt a lot.
Look at it this way, Puppy I is the first grade for the pups. Do you want your pup to have a first grade education? Obviously not, you want her to be a graduate

To achieve this, you can home school, but what will your pup miss out on? Social skills. When the puppy has learnt this, you can teach her new things at home. But the foundations have to be laid in class.
Let me know if you need another argument to help persuade the dh...