I think one of the most poignant parts of the whole book comes as the creature relates his struggles to make sense of who he is and his identity during his time with the De Lacey family. Of course, at this stage he has experienced the way that his physical appearance makes him abhorrent to humans, but note the questions that he begins to ask himself as he learns from the De Laceys:
"But where were my friends and relations? No father had watched my infant days, no mother had blessed me with smiles and caresses; or if they had, all my past life was now a blot, a blind vacancy in which I distinguished nothing. From my earliest remembrance I had been as I then was in height and proportion. I had never yet seen a being resembling me, or who claimed any intercourse with me. What was I? The question again recurred, to be answered only with groans."
We see here the creature desperately trying to make sense of himself, and failing dismally. Clearly the fact that he had never seen another creature with the same physical appearance indicates massive conflict regarding the way he has been made to look. This is heightened by the rejection of the De Lacey's when he does reveal himself, as he realises that his creator had made him to have the same desire for human companionship as humans, but had also given him a phsyical appearance that made such companionship impossible. This is why of course he demands that Frankenstein make him a mate.