I carry a pistol quite often when hunting with rifle..
It's not that I don't trust my skills with rifle at all. Often I'll go from scoped rifle territory to thick brush. A scoped rifle is almost useless there. So, the open sighted .357 or 44mag comes in handy. I've shot deer at close range with pistol while rifle was still in the other hand. I finished off a Bear with pistol after I hit him with rifle round. Yes, it's extra weight, but shooting the head off a Grouse is much easier with pistol than scoped rifle at close range. Occasionally I'll just carry a .22 pistol or my 1911, just for small game while hunting big game. For safey, in Bear or Kitty cat country in thick terrain, the pistol brings piece of mind. It's more of an effective signal tool too.
Other times, I've been known to leave camp, leaving the rifle behind, just hunting the brush with SBH or RH in .44mag. Been successful several times with open sighted pistol too.
-Steve