A controversial theory introduced by August Derleth in his story The Return of Hastur that each Great Old One was somehow tied to or represented one of the classical elements of Earth, Air, Fire and Water. In his scheme, Cthulhu became a water deity due to his association with the ocean depths and Hastur an air deity through his association with the stars. Further, he used theory to justify his setting of Cthulhu and Hastur as enemies. Many writers and fans have attacked the theory on the grounds that it is too supernatural and that the thinking is flawed (on the basis that Cthulhu is trapped under water, ruling out any direct control of the element). However, such criticism fails to look at the theory within the context of the fiction - not only is it plausible for characters in a story to create such a theory and be wrong, but it actually is exactly the sort of theory that should be found in ancient and medieval interpretations of The Cthulhu Mythos. The fact that Cthulhu is found under water and looks like a squid would easily suggest such a link, especially as his entrapment is usually blamed upon the stars and not the fact he is under water. Whether there is any truth to the claim that Hastur and Cthulhu are enemies is unclear - any seeming animosity could be mere coincidence - and the cause is probably beyond mere human comprehension.
See Truth and the Mythos for further discussion of such concepts.