Fatal Flaw

"I don't know, Percy, but every hero has one. If you don't find it and learn to control it ... well, they don't call it 'fatal' for nothing."

- Annabeth Chase talking about fatal flaws

Fatal Flaws are mental or physical weaknesses that demigods, humans, and immortals possess. These flaws can often cause the downfall of the being, but are particularly dangerous to demigods. In Greek plays, they are often referred to as 'Tragic Flaws'.

Description
Fatal Flaws are first mentioned in The Sea of Monsters when Annabeth Chase wants to listen to the Siren's song to learn her fatal flaw. She then explains to Percy Jackson what fatal flaws are. Fatal flaws are mentioned frequently throughout the series. Percy's flaw is personal loyalty, which was told to him by Athena in The Titan's Curse. She says it is a dangerous flaw for the hero of the Great Prophecy to possess, possibly because it means he would "sacrifice the world" to save someone he really cares about. Athena also mentions that flaws that have a good motive are usually the most dangerous ones. They are often the same for demigod children of the same godly origin.

Siren's Music
The Siren's music has an oral hypnotic effect. When the Sirens sing, they sometimes reveal your fatal flaw. Flaws can produce an enticing image which is what lure sailors and adventurers to their deaths, either by drowning, being eaten by the Sirens, or by hitting the sharp rocks (and in modern times, mines) surrounding the island. When Annabeth and Percy are passing by their island, she asks him to tie her to the mast so she can hear the song but not escape to her death. However, after hearing the song, she manages to cut herself free with her knife and dives overboard because of the Siren's hypnotic song. When Percy goes to save her, he sees her vision. She thinks she can fix Luke Castellan, and bring her mother and father back together again, essentially. This is due to her fatal flaw, hubris or deadly pride.

Known Fatal Flaws

 * Percy Jackson: His fatal flaw is excessive personal loyalty. He will risk his life for anyone; his friends, family, strangers, and sometimes even his enemies (like when he warned enemy demigods the Princess Andromeda was about to explode).
 * Annabeth Chase: Her fatal flaw is hubris, deadly pride. She thinks she can do anything better than everyone, even the gods, such as saving her family (seen in The Sea of Monsters when she heard the Siren's music). Annabeth also says that many children of Athena share the same fatal flaw.
 * Nico di Angelo: His fatal flaw is holding grudges. He will hold a grudge even if it costs him his own life. In The Battle of the Labyrinth, his deceased sister, Bianca di Angelo, tells him that holding grudges is very dangerous for children of Hades.
 * Thalia Grace: Her fatal flaw is ambition. She desires power even though she knows she does not need it.
 * Leo Valdez: His fatal flaw is a feeling of inferiority. He always feels like he's the least important, even in the team of seven demigods, he feels that he is the "seventh wheel." He covers this up with comedy.
 * Drew Tanaka: Her fatal flaw is vanity, or excessive pride in one's appearance, qualities, abilities, and achievements. She shares this flaw among many other children of Aphrodite.
 * Arachne: Her fatal flaw is hubris, deadly pride. She thinks she can do anything (weaving, in her case) better than everyone else, even the gods. This resulted into Athena turning her into a monster spider. She shares this flaw with Annabeth Chase.
 * Pandora: Her fatal flaw was curiosity. When she was given the pithos from the gods, her curiosity made her open the pithos, which she was ordered not to do.
 * Michael Varus: His fatal flaws are ambition and hubris. He showed ambition when he chose to journey to Alaska to solve the Prophecy of Seven, and he demonstrated the latter when ignoring the current augur's advice that the prophecy was not for him.
 * Odysseus: His fatal flaw was hubris. This was shown by his encounter with Polyphemus, when declared his true name after escaping the island, and by this statement that he won the Trojan War by himself, without any help from a god. Both of these brought the wrath of Poseidon upon him.

Trivia

 * It is stated by Athena that the most dangerous flaws are those that are good in moderation. In Percy's case, it is good to be loyal to your friends, but being overly loyal could cause the destruction of Olympus or make you predictable to your enemies.
 * Of all the known Fatal Flaws, hubris is seen to be the most common throughout the series.