I was watching Search for Spock with a friend, and I realized that the TWOK tie-ins are all well and good, but when YoungKirk finds OldSpock in the cave in Star Trek 2009, and OldSpock says "I have been, and always shall be, your friend," he's not talking about the day he sacrificed himself to save a boatload of proverbial babies, but the day Kirk made the same choice he was being forced to make - the day Kirk brought him back from the dead.
Let's face it, the battle was lost the minute David Marcus died. Kirk was literally in a puddle on the floor and no one not no one would have blamed him if he refused to lose anything else at that point. Saavik was very clear, in an unclear way, that Spock wasn't alive, mentally, and there was no way to know what it was, exactly, that McCoy had. His son had just died and his ship was disabled, and no one would have blamed him if they had just found a nice safe place to hide and tried to take the ship back while making repairs, then turned tail and run. They would have survived too, because they always did. Kruge was going to kill Saavik and he was going to kill Spock, not that Spock would have really understood what was happening, that's if the ground didn't collapse under them before he got around to it.
Kirk was called to make a choice: when the whole world falls apart, and you can choose to take only one thing with you, what do you choose?
He chose to go to Spock and trust the rest to sort it out.
Flash forward to 2009, in the ice cave.
Spock has lost everything. His life's work died with Romulus. His family, as far as he knows, died on Vulcan. And then one man wanders through his life, and he has a choice. He can use this one man as an opportunity to go back and try fight Nero himself. Or...
Or he can choose to finally repay the man who chose him in the same situation.
"I have been, and always will be, your friend."
Kirk was right. Spock did the same for him.