She joined the hands of Elizabeth and myself. “My children,” she said, “my firmest hopes of future happiness were placed on the prospect of your union.”

Victor's mother Caroline speaks these words to Victor and Elizbeth on her deathbed in Chapter 3. Her dying wish is that Victor and Elizabeth get married, emphasizing how deeply she values family unity. Her words highlight the strong familial bonds and idealized domestic expectations that shape Victor’s upbringing.

Elizabeth, my love, you must supply my place to my younger children.

A bit later in Chapter 3, Caroline makes this demand of Elizabeth. The quote and its implications regarding the responsibilities of parents and children is discussed in Quotes by Character: Elizabeth.

Such were the professor’s words—rather let me say such the words of the fate—enounced to destroy me.

In this quote from Chapter 3, Victor describes his reaction to the words of one of his professors, M. Waldman. During a class lecture, Waldman states that the "modern masters" of science "...have acquired new and almost unlimited powers; they can command the thunders of heaven, mimic the earthquake, and even mock the invisible world with its own shadows." This claim inspires Victor to embrace his dangerous ambition and attempt to discover the secret to creating life, an instinct that eventually results in the destruction of everything he holds dear. When Victor refers to his professor's speech as the "words of fate," he implies that they were a turning point in his tragic destiny. He also suggests that his fate was inevitable, as if there was no way he could have avoided the terrible consequences of his experiments. By saying this, he's already introducing the idea that he doesn't hold the ultimate responsibility for the awful results of his many mistakes.

So much has been done, exclaimed the soul of Frankenstein—more, far more, will I achieve; treading in the steps already marked, I will pioneer a new way, explore unknown powers, and unfold to the world the deepest mysteries of creation.

The suggestion that Victor is using fate, science, or ambition (or all three) to excuse his arrogance and lack of empathy or humanity is bolstered by his words here from Chapter 3. Read more about this quote in Famous Quotes Explained as well as in Quotes by Theme: The Consequences of Ambition.