Why do you think that Santiago loved turtles?

Santiago despises the Portuguese man o' war. The turtles eat these jellyfish, "filaments and all," and this is one of the main reasons he likes the turtles. As an older man who still prides himself on his strength and endurance, he feels a kinship with and has respect for these turtles because they can eat the very poisonous Portuguese man o' war without being injured or poisoned.
Santiago respects the marlin he battles with. It is a graceful and powerful animal and he recognizes this. Likewise, he admires the green turtles and hawk-bills for their "elegance and speed and their great value." It seems that Santiago also admires the turtles because they can live to a ripe old age. As an old man himself, they probably give him comfort that a fellow creature can live a long life and still be effective. Just as Santiago respects and relates to the marlin, he has a similar kinship with the turtles. He notes how their hearts still beat after they're killed and how their weathered hands and feet resemble his own aged hands:

But the old man thought, I have such a heart too and my feet and hands are like theirs.