It is the insensitivity of mankind and the abandonment at the hands of the creator that makes the monster change. There are many steps to the epiphany the monster has. First, he observes the De Lacey's, and is happy to see them loving and caring for each other. However, he craves the same companionship and realizes, in his reflection, how different he is.
Then, he reads some of the books in the De Lacey's shed, including Paradist Lost. In this book, he learns of God's rejection of Satan, and God's punishment for Adam and Eve. When he subsequently finds Victor's journal, the monster first learns that he himself was abandoned, and he is filled with anger.
Then, when he enters the De Lacey's house, to first be welcomed by the old man but then rejected by the family who can fully see him, the monster fully understands his isolation, and vows revenge.
Here are his own words on the matter when he meets up with Victor:
“All men hate the wretched; how, then, must I be hated, who am miserable beyond all living things! Yet you, my creator, detest and spurn me, thy creature, to whom thou art bound by ties only dissoluble by the annihilation of one of us. You purpose to kill me. How dare you sport thus with life?"
Okay, first of all, please be careful with your citations--the monster in Frankenstein never says these words; this line comes from the monster created in Philip Pullman's adaptation of the novel into a children's play. But to answer your question--on the plot-level of the play, Pullman's monster changes his nature from "goodwill" to "Revenge" because he gives up on man's good nature after Felix misreads the monster's threat to Agatha, shoots him, and ignores Agatha's pleas for the monster's goodness. In-essence, the monster's "fine, then!" type of decision--if you want me to be evil, I'll be evil--reveals the monster's despair and hopelessness in a world that as Agatha notes, does not accept the "outcast" (131). However, on an ironic level, Pullman stages behavior that undercuts the monster's innocent cries with familiar symbols of bad luck and sin: the monster breaks a mirror and hands Agatha an apple (129-30). So on this second level, Pullman gives the monster some depth and opens the dark possibility that the monster does not so much change as become.
Hope this helps,