Why is everyone assuming that the cat has a deep meaning?

Perhaps because it's featured in so many scenes. It seems unlikely that the Coen Brothers would've focused so much attention on the cat, unless they intended for the cat to be a pointer to some wider overall significance. Or perhaps you feel that the movie is largely about some guitar-strummin' dude who spends an inordinate amount of time chasing after cats?

So you're in touch with the Coen Bros, you and they go way back and they share all their artistic secrets with you?

Here is why:
When Llewyn is laying on Jim & Jean's couch right before the cat escapes the apartment, he asks: "What's your name again?" To which the cat vocalizes something like "Llewyn" (which, btw, is not a typical cat meowing sound either). There's your answer!
Has anybody else noticed this?

You plebs, the cat is a metaphor of his music career. Its spells itself out when Llewyn leaves her behind in the car.

Do I have to give it to you?

[deleted]

and Terminators are just robots. Hopefully you grew some hair on your balls and are starting to understand cinema 6 yrs later.