Santiago feels a kinship with the turtles because his hands and feet are like theirs, horny and hard. The turtles are tough and impervious to the stings of the treacherous jellyfish, just as Santiago is to the stings of the sea (and more largely to the stings of nature). Like the turtles, he won't give up. He and the armored turtles are part of the pre-ordained order of things, made of the same stuff. The turtles do what they have to do simply because, existentially, that is what they were made to do, and so does Santiago. Like Santiago, the turtles are real and solid, and they challenge what is false, represented by the stinging jellyfish:
The iridescent bubbles were beautiful. But they were the falsest thing in the sea and the old man loved to see the big sea turtles eating them. The turtles saw them, approached them from the front, then shut their eyes so they were completely carapaced and ate them filaments and all. The old man loved to see the turtles eat them and he loved to walk on them on the beach after a storm and hear them pop when he stepped on them with the horny soles of his feet.
Santiago also says he has a heart like the turtle's, that will "beat for hours after he has been cut up and butchered." Both the turtle and Santiago symbolize what is hard and impenetrable on the outside but pulses beneath the surface with hidden, stubborn life (hearts that won't stop beating).