That explains about loathing (4)
I believe the answer is:
hate
'loathing' is the definition.
(loathing is hatred)
'that explains about' is the wordplay.
'about' indicates the answer is hidden within the clue (the clue goes around or about the answer).
'HATE' can be found hidden inside 'that explains'.
(Other definitions for hate that I've seen before include "Fury" , "Extreme dislike" , "Abominate" , "Abhor" , "powerful emotion" .)