In some fanfiction, Percy's motive could be power. He may have grown tired of being at the mercy of the gods and decides that by eliminating them, he can become the most powerful being. Or perhaps he is influenced by some external force, like a dark magic or an evil entity that convinces him that killing the gods is the right thing to do. Also, if he witnesses the gods' indifference towards the suffering of mortals or demigods on a large scale, his sense of justice could lead him to take this extreme step.
Maybe he wants to change the system. Percy has always been a bit of a rebel, and in fanfiction, he could see the gods' rule as corrupt or unfair. So, killing them could be his way of starting anew and creating a better world for demigods and mortals alike. Another motive could be to prevent a greater evil. If he discovers that the gods are planning something that would destroy the world, he might decide that killing them is the only way to stop it.
Maybe Percy unknowingly breaks some ancient and very strict laws of the Gods. For example, he might interfere with some sacred rituals or places that are off - limits to mortals, even demigods like him. In the fanfiction world, the Gods could be very unforgiving when it comes to such violations and decide to kill him as a result.
One possible motive could be a sense of betrayal. If the gods had broken promises to Percy or his friends too many times, he might feel pushed to the edge. For example, if they failed to protect his loved ones despite his loyalty and service to them in previous adventures.
It could also be about power. Percy might realize that with Zeus out of the way, he can reshape the world of the gods in a more just and fair way. He could believe that Zeus's rule is corrupt and that killing him is the only way to bring about real change.
One possible motive could be some sort of mind control. Maybe a powerful enemy has the ability to control Percy's actions and forces him to go after Artemis. This would add an element of tragedy as Percy would be acting against his will.
In this kind of fanfiction, it might be related to the idea that Percy has a connection to a primordial force. This force could have been around before the gods came into being. For example, if Percy has a link to the very essence of the universe that was there before the gods were created, it could make him seem older in a very fundamental way. This could also tie into his powers, like his control over water. If water is seen as a more ancient element than the gods themselves in the context of the story, his power over it could contribute to this idea of being older.
Well, it could start with Percy being framed for a crime he didn't commit by the gods. This false accusation makes him feel extremely betrayed. He then has to go on the run while trying to prove his innocence. Along the way, he meets other outcasts and together they form a resistance against the gods. They might try to find a way to hold the gods accountable for their actions and create a new order where demigods are treated more fairly.
Perhaps he has lost too many people close to him. If his friends, like Annabeth or Grover, were to die in a particularly tragic way, he could be so grief - stricken that he no longer wants to live in a world without them. He might think that death is the only way to escape the pain of their loss.
Differing ideologies during the wizarding war. If James was seen as a threat to Snape's side (even if Snape was on the wrong side, from a moral perspective), Snape could justify killing him. For example, if James was too aggressive in fighting the Death Eaters and Snape thought it would lead to more bloodshed, he might take matters into his own hands to stop James.
One possible motive could be revenge. The Dursleys treated Harry awfully for years, so in fanfiction, he might reach a breaking point. Another could be self - defense if the Dursleys in the fanfiction were to take their abuse to an extreme level.
One possible motive could be jealousy. Hermione is highly intelligent and often outshines Draco in academics. In a twisted version of a rivalry, Draco's envy could turn into a deadly hatred. Another could be his family's influence. If the Malfoys push him to take extreme actions against Muggle - borns, Hermione would be a prime target.