How can I make it more plain ? You are hunting. You have your gun in your hands and an animal in front of you. Provided you have the least amount of know-how, the animal does not see you as a menace and is not armed. It will not retaliate. You are unbelievably safe. No life depends on you shooting this animal before it shoots back at your platoon.
A military rifle is thought out and designed for a situation where gunshots are exchanged, sight acquisition is fast and fire rate high. Two or three lost bullets are no big deal if you hit the enemy enough with what's in your magazine so that you can take control of the situation.
A hunting rifle on the other hand, is thought out for the situation where there is no danger. You do not want to hurt or disable the animal, you want to put it down for meat. You do not want it to leave the premises and let you take over, you want it's body for meals (and some of you trophies). Fast sight acquisition is not as much a priority as precision, and you should make every bullet count. You have (almost) all the time in the world, and even a second and third chance with another animal in your sector, if need be.
It is a wholly different situation, your mindset will be wholly different, so will be how your body act.