I have read most replies, and I think I have a relatively unique opinion on this. First the short answers:

Are you a monster? No.
Should he play football? No.

I have read many replies along the lines of "accidents will happen anyway", "all sports are dangerous to some degree". Etc.
While true, I think one should take into account that american football, as well as hockey, are sports that to some degree include violence in the game itself. For me, that has been that main deciding factor when my son wanted to play hockey. I think the risks are too great as tackling (and other forms of violence) is common and quite integral to the sport.

With that said, he rides skateboard (street, ramp and bowl), downhill mountain bike (lift assisted in bike parks), etc.
So we do take our fair share of risks.

But again, I think there is a big difference between suffering an accident and repeatedly participating in a sport in which violence is a planned ingredient.

Hockey? Absolutely.
Skateboarding? Nope.

The difference between them is that in one you encounter injury risk when something goes wrong, which you try to avoid. In the other violence (dishing it out or taking it) is a core part of the sport.