It's all to do with worth, init?
A rat's ass is pretty worthless, as (certainly in the old days, when rat's were the scourge of society) they were in abundance.

However, some people say "I couldn't give a flying fuck"!
Now, I personally would like to try a flyin fuck, as the imagery that I've conjured up is quite interesting...hmmm...maybe I should try dating a trapeze artist?