Why did Max leave the Citadel at the end of Mad Max Fury Road?
In a world full of trouble and strife, he has the opportunity to step into that and fight against them. He can't just stay in one because he’s a reluctant hero, one who doesn’t want to get involved initially, who only wants to look out for number one, but is moved by forces greater than himself to intervene.
Mad is both on a quest to find himself, his better self, and outrun his past. In 1979’s Mad Max, Max, played by Mel Gibson, loses his wife and infant son to a vicious motorcycle gang headed by Toecutter (Hugh Keays-Byrne, who also plays the villain Immortan Joe in Fury Road). In a ruined world already tearing itself apart, this was the last thing tethering Max to the remnants of civilization, and severing that final tie set him adrift, which we subsequently saw in The Road Warrior and Beyond Thunderdome.
On one hand, he floats through this desolate existence, just surviving. But on the other, as we see in Fury Road, as well as the earlier films, the flame of who he once was still burns inside of him—he was a cop, a husband, a father, a good man—which is the part of him that won’t let him walk away from trouble.
He wants to get away, to be left alone with his pain and his memories, but at the same time he can’t stand aside and not help when he’s needed. The lasting impression and legacy of his family (though in Fury Road he flashes back to a little girl, not his son, which potentially indicates further loss and trauma, and there are some interesting fan theories floating around about that particular tidbit), his wife’s belief that he is still a good man, is what drives him forward.
He may not go looking to play the hero, or just to help as is the case in Fury Road, but in a world full of trouble and strife, he has the opportunity to step into that role. With Immortan Joe toppled, with a good and just and strong leader like Furiosa installed at the Citadel, and the wives safe, his job, for lack of a better word, is done, and he’s free to ride off... and likely be a reluctant hero once again.
At the end, he just disappears, melting into a crowd, on the road to his next post-apocalyptic adventure, and all we’re left with is a mysterious quote.
The last thing we see before the credits begin is a black screen with a quote that reads:
"Where must we go, we who wander this wasteland, in search of our better selves?"
-The First History Man