In the 70s and 80s, gay men adapted animal terms for themselves. Animals have certain appearances and personality traits that they adapted or stereotyped to the point that it became easily recognized terms for others in the community. In the past, people had to be much more discreet about being gay and discreet about what they were looking for. For some reason, using animal traits was part of what they thought to do as the best way to get across what they were looking for physically in a romantic partner or a hook up and what they look like also in a way thats discreet and might only be understood by others in the community.
Historically, San Francisco also had meetings were gay men would meet up for "physical activities" with each other and theses were called "bear hug parties"... Such meetings probably further influced gay men to go by animal terms if they weren't already. On top of that, there was pro gay magazine articles that shared/speard the animal terminology for gay men to use. It just became the discreet/helpful way for gay men.
Now with the modern world, even if more people are openly gay, it's still seen as helpful for dating as a quick way to describe what you are looking for or what you look like.