My response to the mentioned development person was that no, fish mouths are very different than ours. We have sensitive mouths great for kissing and such. Fish have mouths used for capturing, crushing, killing other often spiny and bony creatures.
Now...that said, I believe there are more sensitive places in a fish's mouth than the mandibles. I've had fish react violently to hook-ups that appeared to create a greater reaction than I expected. This always entails a large hook driven through the snout or nostrils. Sometimes a hook impales an eye. I've responded by limiting hook sizes in accordance with the fish I might catch in a given water. A #2 streamer hook is rather likely to impale a 13inch trout through the eye. A #6 can do the same to a 7incher. I do not want to damage the fish I catch, especially if it induces pain, whether it is akin to our pain or not. In waters fished so often the fish develop mutilated jaws, I fish elsewhere. I choose not to participate in that. This is partly an aesthetic, as well as an emotional, sensitivity.
But emotional sensitivity I see as having become particularly skewed in our culture. Few of us have day to day experiences with death, or nature. We protect ourselves and our children from anything harsh. We are able to do so. Lucky us. I see a lot of this as pure inexperience, resulting in an immature, even stunted, understanding of the nature of life. When my son was three, If I were to have dropped one of his plush toys, he'd have exploded into tears. He even hated to throw ANYTHING away in the trash, feeling sorry for the scrap of paper! I see that development person mentioned above as greatly underexposed to reality. She's still protecting herself. And she was eating a chicken sandwich while we talked.
When we first got chickens my wife had a hard time eating eggs she saw squeezed from the cloaca of a bird! She had to get used to it. She's an old hand now. She actually helped me dismember a deer in the woods this fall. And she said, "You know, it didn't gross me out at all now. I was actually excited to get home and get those tenderloins in an iron skillet. Of course, experience can repulse too, and my wife explains that knowledge, her interest and reading on the subject, opened the door and saw her through the "disgust" inherent in the reality that we are animals too.
As to WB's question: I'd stop if every, or most, fish I hooked shed tears and squalled like a mammalian baby, obviously in need of good old comforting. But that hasn't been my experience with fish. And it hasn't been my experience with hunting either, as I've taken seriously my skills and judgment. That too is an aesthetic and emotional sensitivity. Call me human.
Then again, I regularly feed baby mice to the snake in my wife's elementary school classroom. The little mice are cute, and they squeak when they get grabbed by the snake. I feel for them, but will not allow such feelings to interfere. I don't believe that snakes are evil, and know when I let the snake go, it'll do the same thing to wild mice.
The children are not in the classroom when the snake is fed mice. Although they are there to watch it devour goldfish -a good introductory lesson in the way nature works -one of the reasons my wife has a snake in classroom to begin with. Few urbanized children get to see such things and it is quite a shock, at first. If feeding the snake was left up to them, it wouldn't happen. And that isn't right. Confusing? I hope not so far as to cause the eyes and mind to clamp shut.
Being human we are sensitive to others and this is a reality, and a "good" thing for such obligately social animals. Projecting this to other animals makes sense, provides good lessons, and feels right. And I do it too. But, to be intellectually honest, I cannot deny the nature of life. I have gotten over much of the squeamishness, and gained real experience with nature, and in the process been given the opportunity to better know my place in it.