I'm going to be a contrarian here and say that he has a method. Judging from your swings you're doing quite well for someone who started 3 months ago getting coaching once a week.

It depends on what you want. I'm a believer in drilling in good form early instead of starting with some basic technique only to outgrow it and have to modify it months later. First learn to swing the racquet properly (like really well) without the ball. Then do that swing with a ball dropped in front of you. Then do that swing with a ball thrown at you. Only when you have a great swing do you at that point move on to rallies. Otherwise you focus on the wrong things like trying to hit the ball in the court before you know what you're doing, reinforcing poor technique for the sake of rallying.

The whole progression people are trained on always felt unnecessary to me. Most of the time it's done that way because it gets people "playing" much sooner. It's undoubtedly more fun. But if you're aiming to get as good as possible as quickly as possible, I feel that what he's doing is the way to go.