I would advise pushing the pause button with this CFI and ask to see his syllabus for teaching you. And if he is unwilling or unable to produce the lesson plan, or flat says "I don't need a written plan, it's all in my head", then really question if this is the guy you want to spend all this money with.
Based upon my experience with Ron Levy and the PIC program, there are hours and hours and hours of foundational work before you can start approaches. All of it builds toward doing approaches. But there are many skills to master first and much knowledge to take on board.
For the student, it's difficult to recognize you might be experiencing a disservice, since "you don't know what you don't now."
But approaches now..... you haven't been shown what's needed to stay ahead of the airplane, how to configure BEFORE you're on the approach, how to properly intercept and track the radial, how to properly enter and execute a miss approach hold, and more. And these are just a small few of the items you need to know before you do approaches....
Again... talk with the CFI and ask to see his lesson plan, then discuss the what why and when of it. Don't be afraid to ask questions about the sequence. If the answers aren't to your liking, then you will have more data to make a decision.