The Creature, feeling utterly alone and miserable, believes that a companion who is like him would alleviate his loneliness and make him feel less monstrous. He argues that having someone to share his experiences and burdens with would make his existence more bearable.
This is the central theme of their encounter. The Creature is not seeking revenge at this point, though that will become a driving force later in the story. His primary motivation is the desperate hope for companionship and acceptance.