2024's "Godzilla x Kong: The New Empire" reveals that the longstanding enmity between Godzilla and Kong in the MonsterVerse is deeply rooted in their species' brutal history.
Godzilla's species, which has existed for millions of years, was nearly wiped out by MUTOs (the creatures from 2014's "Godzilla") and fought a fierce war against Kong's kind.
During this war, the Skar King led Kong's species and used an enslaved Titan named Shimo to kill many of Godzilla's kind before attempting to conquer the surface world.
It was Godzilla who ultimately defeated the Skar King, imprisoning him and his forces in the Hollow Earth, thereby saving the surface world from complete domination.
This historical conflict explains Godzilla's inherent animosity toward Kong and his species, who were partly responsible for the near extinction of Godzilla's kind.