These incidents were exciting, but at no time did I fear for my life, and never even considered shooting the animal... of course if I ever did truly feel threatened I would not hesitate squeezing the trigger. I have had many similar scenarios with bears as well.
My FIL had more encounters than he could count, but only had one instance where he feared for his life.
They had shot a cow who eventually dropped in a swampy point along the river. It’s about 12 inches of water there, 3 yards to the river, and 25 yards to anything bigger than reeds. Him and his buddy hung their rifles and gear on the trees at the edge and went to start working. They got to the cow and had barely started when a pissed off bull popped out of the bush beside their rifles.
It charged and the choice pretty well became... take your chances possibly getting trampled and drowning in a foot of water, or take your chances with the river.
FIL dove in and headed straight across, his buddy narrowly missed a swinging antler before diving in and tried to just go down river. It chased him along the edge until he finally crossed.
On the bright side, it was sunny, mid day and they were on the right side of the river for the cabin. On the not so bright side, they were soaking wet, it was right around zero degrees, and the cabin was still at least 1.5hrs of bushwhacking and snowmobile trails away.
Luckily there was an old trapper who had a camp just down river. They ended up hiking down to it. He was out there, so everything was already opened up and warm. You can imagine his surprise coming back to camp and finding two half naked guys inside trying to dry out and warm up.
Every year afterwards they would make sure his wood pile was well stocked for the winter.