In God of War II Kratos was still bitter because the gods never relieved him of his painful memories as they promised so he took his frustration out on whatever
Zeus sees Kratos as a threat to him afraid that he'll do to Zeus what Zeus did to Cronos and plus Kratos was attacking a city he shouldn't have attacked so Zeus saw it necessary took Kratos' powers and kill him leading to Kratos cheating death. On his journey for revenge, Kratos learns more about the great war and the Olympians
He decides to destroy Zeus not just for revenge but because the gods have shown time and time again that they're liars and cowards only looking for their own gain (minus Athena which is why Kratos felt bad upon killing her) he decides to put an end to it.
Kratos has proven that he can escape the fates set upon man by the gods and goes on with the idea that mankind doesn't need such beings ruling over them, he turns to the titans and thus reignites the great war. I also believe that he's looking for redemption himself and believes destroying the Olympians will grant him peace
Atleast that's what I got from it
