In large part, the nature of the monster's creation served to condemn him forever to the status of monster despite his having a human "soul" or the ability to feel and think like a human. His enormous size and super-human strength, which give far greater impact to his rage-driven killings, also serve to make him repugnant and anathema to humans so that he is considered a monster rather than a human.
His appearance, having been cobbled together from cadavers, is another reason why he is accorded the status of a monster rather than a human. Even as he comes more and more to feel the emotions and the desires of humans, love, sadness, loneliness, etc., humans cannot look on him with anything other than fear and loathing. This compounds his loneliness and fear, which then drive him to more "monstrous" behaviors, further condemning him.