The creature wanted validation as a human being from a human being. Regardless of his most immediate origin, the creature was created from human flesh. To get technical, his DNA was that of a human (though of course DNA was unknown at that time). Yet Victor consistently thinks of him as "non-human." In time, the creature comes to agree with him, seeing himself as opposed to those humans who consistently rejected him.
The creature also wanted instruction from Victor. Since Victor immediately deserted him, this was denied the creature, so he sought it elsewhere. Yet on the discovery of Victor's notes in the pocket of the greatcoat, the creature did learn from Victor, yet not in the way either would have wanted.
Companionship was another request of the creature. Since Victor refused to grant him this, the creature demanded that Victor create a woman for him, someone with whom he could travel away from the human world and seek the solace found in the presence of someone like himself.
Above all, the creature wanted love, the love due to a creature from his creator. The creature knew what love was. As Shelley displayed the Enlightenment philosophy that man is born good, the creature was born with an inate ability to love and a need to be loved. Monsters are created when society denies an individual this love, as Victor did to the creature. Victor's scientific skill made a creature. His rejection created a monster.