This quotation is actually not from Mary Shelley's novel, but, rather, it comes from Kenneth Branagh's film adaptation of the book starring himself as Victor Frankenstein and Robert De Niro as the monster. The movie was released in 1994, and to be frank, it is not a very good adaptation of the novel; it seems, to me, to be intended as a horror film rather than a movie adaptation of an existing work. There are several scenes of gratuitous horror designed only to be revolting -- most especially including the "mate" Victor fashions for his creature (there is a twist here that I am loathe to reveal) and her response to realizing what she is.
At any rate, this particular line does seem to encapsulate many of the ideas that the creature expresses to Victor during his request for a mate. He says, in part, in Volume II, Chapter IX,
I will revenge my injuries: if I cannot inspire love, I will cause fear; and chiefly towards you my arch-enemy, because my creator, do I swear inextinguishable hatred.
The creature has tried to be loving: to the De Laceys, to the drowning girl in the forest, and it has only ever blown up in his face. He is met with hatred everywhere he turns. He claims that he began life with "benevolence and generosity" (Vol. II, Ch. VII). But now, however, having been neglected and abused and insulted in every possible way, if his creator will not give him this one chance at a loving relationship, then he will work toward Victor's destruction.
Just as the creature identified humankind as a species that was capable of great good and great evil, we now see this dichotomy reflected in him. This is probably the best proof we have that he is, indeed, a human being, however frightening and ugly.