We suppose Victor is the primary protagonist, since he is the main person we are concerned with. We see what he wants and we're invested in his character. He also fits the "tragic hero" role as forces outside of his control continually thwart his desires. Well, sort of outside his control.
AND YET, the monster seems more human than any character, including Victor. All the guy wants is compassion and companionship —what's more puppy-dog-protagonist loveable than that? Of all the characters in this story, he is the only one who performs any true acts of grace: he saves the little girl from drowning in the river; he gathers firewood for the peasants at the cottage; he DOESN'T judge people based on their appearances.
In fact, if we read this novel as a creation story, which we sometimes do, the obvious protagonist becomes the monster. He stands in for man confronting the basic human condition of suffering in an indifferent world with an absent God. In this way, we can relate to him far more than to the other characters. They all suffer because they've brought about their own downfall through their own mistakes. (Well, maybe not Elizabeth, although she does make the big mistake of liking Victor.) But the monster was just born with bad luck.