During the Hachinosu Battle, Aokiji finds himself facing Garp, who is attempting to distract the Blackbeard Pirates as to buy Koby and co. a chance to save people.
We see a flashback of Garp’s lesson: if you can only save 2 out of 3 people, those being yourself, a baby and an old man, you save yourself and the baby, as the old man has less future potential.
Most fans saw this apply to Koby leaving Garp behind to save himself and the marines (them being the baby, aka, the weaker of the three), which makes perfect sense, as it shows that Garp’s phylosophy got through to him.
However, I saw something different. Koby isn’t the only student of Garp on the scene, for Aokiji is also there.
Aokiji never once even TRIES to go after Koby and co., and instead chooses to fight Garp. He ends up defeating Garp, his old mentor, at the cost of allowing the marines and Koby to escape.
If we assume Aokiji is indeed planning to betray the Blackbeard Pirates, this could read as follows: Aokiji could not refuse to fight, as it’d blow his cover. Therefore, he can only save two of the three enemies from himself: Koby and co., Garp or the marines.
He applies his mentor’s phylosophy and spares the marines and Koby, while going on to defeat the old man.
To further prove this point, the chapter’s name is “The Final Lesson”, which utterly shows that this is Garp’s final lesson to Aokiji, and possibly entails Aokiji will sacrifice himself in the future as well to someone who he believes to be the future (Robin).
It would make much more sense for it to apply to Aokiji, as Koby will most certainly never be put in a position where he is the old man who has to preserve the future. Koby will find a predicament of the sort, but I believe that he’ll find a way to save all parties, as he did in Marineford, but this time, without sacrificing himself to do it, surpassing his mentor at once by disproving his phylosophy.
Lastly, I believe Garp was laughing because Aokiji had finally completed “The Final Lesson” by choosing to go for Garp, rather than future, which he failed to do previously. In Marineford, Aokiji nearly kills Luffy.
Aokiji will sacrifice himself in the future.