Well, we learned in Re: that Kaneki didn't want to live even before he became a ghoul. I read it as the only thing really keeping him around was Hide.

This was also the reason for his pacifism; he figured that if he could die quietly without hurting anyone, maybe even sacrifice himself, he could be happy. Then Rize came in and he realized that, if he's going to live as a ghoul, and protect those he cares about, he's going to have to fight, even if he hates it. This was when we got Shironeki.

Then, at the battle at the end of TG, Kaneki goes up against Arima in an attempt to protect his friends, and finally gets the death he wants.

...except he doesn't. He dies, yes, but is reborn as Haise. Haise actually quite likes living, and when he gets his memory back Kaneki, is a bit confused. When he fights Arima, he gets the perfect badass death: No one can blame him for losing to Arima, and he sacrificed himself to save his friends. He's cool with this, until He gets a vision of Hide, paralleling Rize. Hide pretty much calls Kaneki on his bullshit here, saying that he can't die just yet, and he'll find a reason to live. The rest is history.

TL;DR Kaneki has wanted to die for pretty much ever now, and wants to do it saving his friends. The fact that he didn't take the perfect opportunity to give up shows that he's grown.