Do Athena and Poseidon hate each other?

yes they did they competed for the city of Athens Athena won by giving them a olive tree and posedion gave them a spring , also he went on a date with medusa in one of her temples [ that was her daughter medusa used to be beautiful and Athena is a goddess of purity so she changed her so no man can never look at her again ]

Hate would be a strong Word for any god-to-god relationship in Greek mythology. The main source of tension between Athena and her uncle was the city of Athens.