In George Meredith's novel The ____, Sir Willoughby Patterne can't see why Clara Middleton doesn't want to marry him (6)
I believe the answer is:
egoist
(Other definitions for egoist that I've seen before include "A seld-centred, conceited person" , "Man who thinks highly of himself" , "Conceited and self-centred person" , "Bighead" , "Self-absorbed person" .)