Why does Luke Castellan betray Camp Half-Blood?

In Percy Jackson and the Olympians: The Lightning Thief, Luke Castellan is the son of one of the gods: Hermes. As a charming, likable, and seemingly upstanding boy with a talent for wielding a sword, Luke seems like the last person to have an evil side. Nonetheless, it is revealed at the end of the novel that Luke has become a servant of Kronos and has served as the motivating force behind much of the conflict of the narrative. 
After being sent on a quest by Hermes to seek the Golden Apple from the tree in the Garden of Hesperides, Luke finds himself humiliated. He is initially pleased that his father has sent him on such a quest, but he begins to lose confidence in himself when he realizes that Hercules has completed this task previously. As a result, Luke fails on the journey and is scratched by the dragon guarding the tree, resulting in a scar on his face. When he returns to Camp Half-Blood, he notices that the other individuals there have begun to pity him. Resentment grows within Luke, who feels that Hermes does not love him. Desperate for revenge, Luke starts thinking about destroying Olympus.
Luke is later contacted by the Lord of the Titans, Kronos, and he joins his cause to destroy Olympus. He also begins to work directly on his behalf. Luke is given the task of stealing the Helm of Darkness (the weapon of Hades) and the Master Bolt (the weapon of Zeus) in order to start a war between the gods.
At the end of the novel, it is revealed that Luke does just that while on a field trip to Mount Olympus. Luke explains to Percy that he believes the gods are poor leaders who behave irresponsibly and that they must be dethroned. 
Thus, we can conclude that Luke betrays Camp Half-Blood and joins forces with Kronos out of resentment for his father, out of feelings of shame that the other campers pity him, and out of a need to make himself feel validated and significant.