Arachnophobia

Arachnophobia is the fear of spiders, this fear is something that all of the children of Athena suffer from. In ancient times there was a girl who was a beautiful weaver of tapestries. This mortal woman boasted so loudly about her beautiful artwork that she captured the attention of Athena. Athena was angry that a mortal would dare compare her work to that of the Gods, and challenged the mortal to a contest.

The mortal woman created a tapestry detailing foolishness of the gods and their cruelties towards mortals. Athena created a tapestry praising the gods for their achievements. When the weaving was finished, the girl continued to brag. Athena, in a fit of rage, turned the girl into a spider. The girl's name was Arachne.

From that point on the children of Athena feared spiders because they worried that each spider was Arachne coming to take revenge. The modern terms Arachnid and Arachnophobia are both derived from this ancient Greek myth.

The Lightning Thief
When Hephaestus' metal spiders attacked Percy and Annabeth, Annabeth got scared.

The Battle of the Labyrinth
Annabeth was scared of the metal spider that led them to Hephaestus.