Hee Hee. I actually laughed at this one. A "LOL" is in order.
Okay, since I’m so nice, the reason is this: Kratos had released “Hope” into himself (which happened in God of War 1)…he used this power to beat Zeus and such. Obviously the whole point of the game was to get “Hope” from Pandora’s Box but we discover that he had it in him the whole time and used it to kill Ares and the other gods along the three games. Anyway, at the end Athena wants Hope to likely use it for her own selfish ends…or at least to make a mean soufflé in the kitchen.
Kratos kills himself for two reasons. For one, his whole reason for being was revenge and now that everyone who he hated was now dead, he had no reason to keep living his torturous life. Plus, Kratos gets a double-bonus since by killing himself he gets to screw over Athena by releasing “Hope” out into the world where it supposedly helps all the regular folks still alive out there rather than giving it to some deity.
Plus I think he secretly had a bad case of hemorrhoids and just couldn’t take it anymore. The total anger, the mood swings, the death wish…it all makes sense.