He didn't actually. Caligula had a banquet at a time when there was an open consul position, and all of the Senators and aristocrats present were discussing who would be appointed. Caligula apparently made some offhand Trump-ish remark like "my horse would make a better consul than any of you" and all of the contemporary (establishment) writers who hated him recorded that as a sign of insanity rather than the epic troll that it was.

Most of the really over-the-top stories about Caligula come from a similar place: embellished by hostile writers to make him seem like a tyrant and a lunatic when he was in fact a populist, not unlike what we see the media doing to Trump. This is exactly the same reason we should take the stories about Elegabalus' degeneracy with a huge grain of salt. You can't really trust contemporary accounts of the behavior of Roman emperors, especially not the ones who were assassinated. Too many people had a vested interest in justifying such a murder by painting the assassinated emperor in the worst possible light.

Caligula didn't trust his senators, so he elected his horse to a major position instead of them. When they asked if it was to get his way, the new senator yelled, "neigh"