One might be conceited however you look at it (3)
I believe the answer is:
pup
I believe this is a double definition.
'one might be conceited' is the first definition.
(pup can mean a conceited young person)
'however you look at it' is the second definition.
(Other definitions for pup that I've seen before include "Produce litter" , "Small palindromic dog" , "Young of various animals" , "Young seal" , "Young animal" .)