It is not unusual for hunters and fisherman to have great respect for the creatures they prey upon. The word "prey" is a key element here, because a part of that reason is that they see themselves as links in the grand food chain of our planet. Humans are an alpha predator to most everything that walks, flies and swims. In the sense of the food chain and the ecosystem, it doesn't mean the higher levels are necessarily better. They're just born to be hunters, just like others are born to be prey. Some are both, like the marlin itself.
Thus, Santiago feels a sort of kinship with the fish. To him, it's not that different from a human, because they share similar experiences. Hunger drives all life on Earth. When a living being, human or fish, wants to eat, they go and find some. On that day, the marlin just happened to be caught and a part of Santiago is sorry for that, because the marlin is such a worthy adversary. It is a great hunter, just like he is. Santiago respects the marlin's wish to live, its will to fight for it. That feeling grows as the marlin tries to trick him and use cleverness instead of brute force. As hours and days go by, Santiago finds that there isn't much that really differentiates him from the marlin. They are both strong, stubborn, ready to suffer and fight for their goal.
Another reason for why many hunters and fisherman have sympathy and respect for animals is that there is no separator between them and their food. Most humans eat fish that someone else has caught, meat that someone else has killed. So for us, the connection between our food and something living is lesser. But Santiago feels the fish with every fibre of his body and being. He feels the marlin fight for its life, feels its desperate struggle and mad anger. It's no wonder he feels compassion and appreciation. His own needs and the needs of the village will come first, since they must eat. But Santiago is grateful to the marlin for its ultimate sacrifice, knowing that if he were prey, caught on a line, he would fight just as fiercely.