The cartilage between the vertebrae is quite strong while the skeleton is fresh, it does not easily fall apart - although I would have thought the shark attacks may have managed it. After the skeleton has a chance to dry the cartilage will shrink and pull away from the bone, and also becomes brittle and easier to break. (This from a man who, as a boy, had a slightly morbid fascination with bones; I used to leave them on ant mounds to get cleaned etc. In primary school I took a steer's skull for "show and tell", but got into trouble because there were Red-back spiders living in it. I knew how to win friends and influence people even then.
)
It seems to me that the story says much about Hemingway the man. There is the "big white hunter" thing that revels in the struggle between man and beast, especially on - what they believe to be - this close to equal footing. But there is also an odd sort of disconnect in his writing style, one that leaves me not really caring all that much. CRussell mentioned love being a theme, and I can see it, but it is love held at a distance, as we might expect from a man of Hemingway's generation and disposition. We might also read into this story: better death than dishonour.
Consider that this was no novice fisherman. As soon as he realised he had hooked a very large fish he had to have known the outcome - every step should have been predictable to him. So why choose to waste this fish that he professed to loving (even as he was trying to kill it)? Because to have loosed the fish would have been to admit defeat. He knew the fish would either kill him or he would kill it (and he admits at one point to not caring which), and he must have known it would be too big to get onboard so he knew that - even if he defeated the marlin - he was going to lose it to sharks. He knew he was going to lose it, but he prefers to waste its life (but see below) and risk his own life, rather than risk returning defeated. ("destroyed but not defeated" he says, but of course the sharks defeat him, making all that struggle seem rather pointless.)
I don't think this really comes into what Hemingway was writing (I don't think he cares), but one thing I'm not certain of is at what point the marlin is as good as dead. I guess that will depend on things we are never told (where the hook bit and so what damage might have occurred if it was torn out), but the answer does potentially impact how you interpret the story. If we count the marlin as "as good as dead" from the moment it it is hooked (even if it breaks the line, I can't imagine it will lead a long life dragging hundreds of feet of line behind it), then everything Santiago does from that point can discount the fish (if not its suffering) because he has already killed it.