It is pretty clear that 'badger' was chosen simply because its opening letter alliterates with the 'b' of 'bum'. Bullock, boar, bear or a multitude of others would have done as well. The bottom ends of many animals - especially the hairier animals - do tend often to reveal evidence of what bottom ends are for...ie they can look rather 'rough' in the sense of crude, unpleasant or nasty! Perhaps the badger fits that description?
The hair on a badger's bum is rough in texture, but he is among the cleanest of animals. He is in fact one of the few to dig latrines and use them regularly. Badgers over the years have been subject of adverse propaganda by people who wish to look justified in baiting them (forcing them to fight with dogs, outnumbered of course). Otherwise, no doubt a different animal would be chosen. Dog's bums for example, do not always look particularly decorative.
"Laughing out loud" or - some claim - "Laugh out loud." The former suggests that the writer is, at that moment, laughing aloud whilst the latter suggests it is an instruction to the reader. Whichever...the idea is that the person is amused.