I actually came to the drums quite late. I was 20 years old when I finally figured out what I wanted to do. My dad didn't make me practice but he certainly encouraged it and even made me cassette tapes of songs, drummers, grooves I needed to learn. I played along with lots of music, anywhere from 4-8 hours a day of practicing. I was older and more focused and determined to get better as fast as possible.
From when I was 3 years old I played piano. At 10 years old my parents sent me to lessons but I really didn't like it so after 7 months or so I burned out and stopped going. It actually put me off music for a couple of years. Striking the balance between keeping it fun and doing the work at the young age is difficult and I'm sure you're doing a great job!
I really don't have a definitive answer for you of what you can or can't do. Just keep finding the balance so he doesn't start to dislike it. Keep listening to good music with him, listen to whatever he likes even if you're not crazy about it and play him all the good stuff!!
All the best,