I know. Season 9 was SO painful to watch.
I get that Sam felt that Dean was honoring his choice or his free will, but, if there's any chance at all, even a bad chance, why would you NOT save a loved one from death? One of the saddest lines in an earlier season was when one of the brothers said, "We have no friends. All our friends are dead." There's not much left for Sam to live for. So he wanted to die. But Dean was still alive. So it's sad that Dean wasn't enough for Sam to want to live.
I also think part of the desperation Dean had in the first episode of Season 9 as Sam lay dying in the hospital was knowing that Sam had to do all those trials instead of Dean. Dean wanted to do them, but failed to kill the hellhound which Sam did, so Sam took on that suffering in his place, in the end not even finishing it because it would have killed him. So ending up dying ANYWAY would make it all pointless. If you died shutting the gates of hell, you achieved something (even as Sam went to the cage to stop the Apocalypse). Or if you gave up shutting the gates of hell but lived on with your family, THAT is something good too. But to not achieve anything and die anyway -- what good would come from that? It would seem so purposeless.
So love and guilt play into this. Another part is perseverance (or stubbornness). You don't give up. You keep fighting. (I'm reminded here of some of Cyrano's final words in Cyrano de Bergerac: "I fight on!"
Sam was surrendering here and Dean didn't want to let him. When Dean wanted to give in to Michael (Sam accused him of committing suicide), Sam and Bobby and Castiel wouldn't let him. And Dean isn't letting Sam give in here when Sam wants to give up. (I know the situations are different because if Dean became Michael's vessel, the Apocalypse would happen and half the planet would die whereas here the only person who would suffer is Dean, but then again, thinking of that, he doesn't have anyone left. And the reason he doesn't have Ben and Lisa is Sam's fault. Soulless Sam turned him into a vampire; planning on having Samuel kill him, Dean goes to see them one last time -- foolish but human -- and ends up pushing Ben away in desperation not to hurt him but angering and alienating Lisa which caused her to break it off with him. So when Sam said in Season 5 to let him make his choice and save the world, Dean had someone to turn to. Now Sam wants to die and it doesn't seem to matter to him that he's leaving Dean alone. I can see that someone would be in such pain that they only think about ending their own pain, not about how much pain they would cause others. But when your loved one steps in to rescue you from yourself, eventually, once you're in a healthier place, you can appreciate what they did.