When one decides to no longer give a shit about something or someone or a certain situation; like the honey badger (See the youtube video-Randall's version- if you don't know the honey badger). The honey badger doesn't give a shit. It's a more "polite" or eloquent way to say "I don't give a shit."
Person 1: Oh man, are you studying for the final, its tomorrow morning!
Person 2: No, I'm taking the honey badger option for this one...
Person 1: Oh my god, did you hear about him/her?!?
Person 2: Nahh...I'm taking the honey badger option for him/her..
Person: I will forever be taking the honey badger option for this class/that person/situation.