There are going to be alot of different answers to this. A few things I enjoy.

The total experience surrounding shooting. The calm before the firing is almost meditative.

The feeling of your primordial instincts. The parts of us we dont acknowledge in modern times but are still there.

There is the meal that follows and the comradery.

There is in some cases like bird hunting where it can be fast and exciting like a irl video game.

With this is the sense of adventure where there is no telling whats coming. No advanced technology to help. Just how good are you on your own.

These are just a few of mine but Im sure there are many others