As long as you too are spending time in the outdoors together, what does it matter what he carries? And just because he is shooting the mathews, why does that mean he can't stump shoot with you?
These are the questions that come to my mind. After all you shoot what you do because of your choice. Give him you reasons why you choose to do the things that you do, but also give him the freedom to make his own choices, too. I think in the end, when you look back on your times spent together in the field, your experiences will far exceed the methods.
My daughter shot her first squirrel this year with a shotgun and it was the highlight of our hunting together so far and it may seem odd to others, but that squirrel is at the taxidermist right now and will be treasured and proudly displayed in our home, even though I personally have never had a deer that I shot with my longbow or recurve, ever professionally mounted.