Victor Frankenstein travels to a remote island in Scotland where he sets about the creation of the second creature for his "monster." As he works, Victor ponders the consequences of his work:
I had been struck senseless by his fiendish threats: but now, for the first time, the wickedness of my promise burst upon me; I shuddered to think that future ages might curse me as their pest, who selfishness had not hesitated to buy its own peace at the price, perhaps, of the existence of the whole human race.
As he works, the creature "a ghastly grin wrinkled his lips" as he marks Victor's progress. Victor notices and expression of "malice and treachery"; he cannot make the creature as he has planned. When the "wretch" witnesses this, he utters "a howl of devilish despair and revenge" and leaves. However, he returns to the cottage where Victor is, telling his creator that he has endured misery as he left Switzerland with him, creeping along the shores of the Rhine, enduring fatigue and cold: "do you dare destroy my hopes?" Victor responds,
"Begone! I do break my promise; never will I create another like yourself, equal in deformity and wickedness."
Still the creature declares himself Victor's "master," threatening to fill Victor's hours with dread and misery, and "soon the bolt will fall which must ravish from you your happiness for ever."(He will be avenged against Victor)
The creature has been alive since early in the book on that fateful November day when Victor brought him to life and then abandoned him in the apartment. However, it is not until meeting the DeLacey family that he is introduced to and truly understands love, beauty, and all that he is denied in life because of his hideous appearance that he becomes fueled by thoughts of revenge and anger toward his "father," Victor Frankenstein. When the creature meets with Victor in the mountains and begins telling his tale in Chapter 11, Victor has fleeting moments of humanity and tenderness toward the creature who murdered his brother William and frames poor Justine for the murder. It is during this visit and the creature's logical, articulate and emotionally charged argument that Victor agrees to create a companion for his "child" so that he will no longer be alone in a world which will not accept him.
In Chapter 20, Victor's fears get the best of him, and rips apart the female creature that he has begun work upon. He has come to the realization that he made a horrible error in playing God and creating the creature, and that he will not make the same error twice. Victor is, for the first time in the novel, prepared to fully and completely take responsibility for his actions instead of retreating into some fever or illness or a hike in the woods. It is as a result of this action--the destroying of the female creature--that the male creature's revenge is ignited and his declaration of revenge is unparalleled. He, in turn, destroys every person Victor loves, therefore, creating a life-long companion for himself...Victor. Both of them live for the other in their unhealthy relationship. The creature cares of Victor by leaving him hints, food, supplies. Victor continues pursuing the creature even when it means imminent death due to his human frailty. Only after Victor is dead, does the creature truly have no other reason to live, and he jumps out of the ships window after bidding his "father" goodbye one last time.
So, the simple answer to your question is revenge. The creature truly comes to life in Chapter 20 as a result of his desire for revenge on Victor Frankenstein.