You must take into account, the Greek Gods are not like Jehovah or other almighty and omniscient Gods, and they're also pretty much like "mortals" in the way they scheme, plot, and just their regular behaviour, as in they're not "saints" and they use their powers on a whim and whatnot, specially very often with great disdain and cruelty when dealing with mortals.
Now take this with a grain of salt if you will, but the following is what I make of the story of God of War :
If you followed the series' story thoroughly, you will know since the first game there's a prophecy that speaks of the Fall of Zeus. I'm really not sure which of the Gods have knowledge of this possible future, but if would seem Zeus' most loyals Hades, Poseidon and Athena are aware of this.
If you remember GOW1, Ares had turned against Zeus' will by the end, and he was defiant and called him his FATHER. It would seem Ares was just expecting Kratos to collect Pandora's box for him so he could use it against Zeus. Not that his plans depended on that, but hey, a little extra power never hurts, and better him than Kratos anyway.
It's possible Zeus was clear the prophecy talked about one of his sons was to bring about the end of Olympus and his death. He knew Kratos was his son, as was Ares. So he just let fate play out, and in turn both his sons would face and kill each other. However it turns out Kratos became a God of sorts (still without a throne though, until he was rewarded with a place in Olympus by Zeus himself) by using Pandora's Box, and he survived. That doesn't mean anything by itself, but I'd think Zeus preferred to have his potential mortal enemy closer (the "keep your enemies closer thing", you know), and also to watch over Kratos further developments.
HOWEVER, Kratos actually had VERY STRONG SUSPICIONS that Zeus was his father. After all HE HEARD THE TRUTH ABOUT IT from his dying mother (which was cursed by Zeus not to even think about telling anybody of it. The moment she intended to tell the demanding Kratos -already the Ghost of Sparta- she transformed into a mindless beast and Kratos killed her, only to hear the word Zeus on her dying breath-). **
So Kratos was used by Zeus and Athena to kill Ares. He gets tricked into doing this task falsely expecting a reward he will never get (either because it's really impossible by the Gods to do what he asks, or they were no longer able to do it since Kratos became "Godly", or Zeus just had further use for him, or they were just plain cruel -remember Kratos was a servant of Ares and did lots of things wrong against Athena specifically, it wouldn't surprise me she was not in a forgiving mood with Kratos- ).
Now Kratos is the God of War, and he was broken. He had to live knowing how with the very powers of the Gods conceded by Pandora's Box he couldn't undo his greatest sin. He had a broken spirit now, and HE KNEW Zeus was behind it all, and Zeus was his father and was so merciless and selfish. He had turned him down, and all Kratos had left in his mind was vengeance. So he rebels against the Gods, and goes against Athena's will, too. The inminent danger revealed, Zeus must take action. But what can he do now? The very balance of Olympus rests on the rule that Gods do not wage war against other Gods. Not even Zeus would dare to break that pact. But he does, kind of. He hurts Kratos causing a partial loss of his powers, but that won't be enough to revert him to a mortal status. So he tricks Kratos into disposing of his own powers himself, with the all-powerful blade that Zeus conjured when he was at the top of his powers: The Blade of Olympus. Kratos pours his powers willingly into the sword, and becomes mortal again. But we know the story doesn't end when Zeus pierces his body with the same Blade. The lingering spirit of the titan Gaia, the everpresent mother of all living things (and stepmother of Zeus), came to his rescue and gave him the strength to escape Hades (once again).
All this wrong-doing against Kratos, against humanity, against the titans, his selfishness, his unresting quest for supremacy by all means including injustice, all those things have rendered Zeus weak. It all started with the Titans. His hate for Cronos his father has been consuming his soul, even Athena knows Zeus is on the wrong path, but she will not dare go against him 'cause she herself says it: Zeus is Olympus. Now Kratos has the power of the Titans, he has brought them back to present time, he wields the sword which ended the Titans and can slay a God.
Right now he's half God, empowered with the might of the titans, his rage has no limit and he will see it all come to an end. He no longer cares for his past, he has no future. Nothing will prevail. Chaos will rise again.
** you will find this secret revealed in a video on the "treasures" section of the first game.