Why did the author of Percy Jackson add the myth of Athena and Arachne in chapter 16?

While Arachne was never seen, it was implied several times that children of Athena have a fear of Arachne's children, the spiders (known as arachnophobia). Annabeth Chase was so scared of spiders that she even has problems with anything that looked like them or even the word spider. When Ares sent Percy Jackson, Annabeth, and Grover Underwood to Waterland, they were attacked by tiny mechanical spiders that were made by Hephaestus. Later, when Annabeth was hypnotized by a SimCity-type game in The Lotus Hotel and Casino, Percy triggered her out of the hypnosis by mentioning the word "spider". You can check this out below:

https://riordan.fandom.com/wiki/Arachne