It all depends the type of hook and where it is stuck into. I had a cousin who pulled a hook through his toe when he went to cast once and by brother hooked me in the shoulder once casting from a boat. both where in really deep and pushing them all the way through was less damaging the trying to yank them out. So i pushed the hook through my cousins toe nail and my brother pushed it back through my shoulder. The final time was when I was stripper fishing and lipped a 37 pounder with a jig still in it's mouth. The fish thrashed and sent one of the treble hooks into my hand. I used the line trick to pull out the #4 treble from my hand.

Country, I keep a bottle of Anbesol in my tackle box. A few drops rubbed in the skin around where the hook is will be deadened. Then if it is a large hook with a big barb, I use the push it through and cut method, but small hooks with small barbs will pull back out without too much pain or tearing. Then always wash and disinfect the wound.