How does the theme of failed father figures shapes the story of Frankenstein. Why might this theme be important to Mary Shelley?
The failed father figure can be seen as central to the story of Frankenstein. When Victor Frankenstein abandons his creation, the hideous composite monster, he is essentially a father abandoning his child. Left to his own devices, the monster, just like a child growing up without a father figure, is rejected from society and is unable to learn how to effectively participate within a community. Thus, the monster's rebellion against Frankenstein can be seen as a manifestation of a classic archetype, a son who, seeing fault in his father, seeks to engineer his father's downfall.
There is another interesting component to this question that bears mentioning. Many scholars also see the monster as a manifestation of Lucifer, the Fallen Angel, while Frankenstein parallels God, the Creator. If we are to look at this metaphor from the perspective of the failed father-son relationship, we arrive at an interesting commentary on God. Perhaps, the novel suggests, Lucifer's rebellion and subsequent fall is actually God's fault, and perhaps God is not an entirely benign Creator after all. While there is by no means a definitive statement about this idea in the novel, it is impossible not to see a suggestion of it, and the very suggestion of such an idea, no matter how subtle, is chilling.
From the very beginning of Mary Shelley's Frankenstein, there is a general absence of familial and parental ties. Right at the beginning, Victor isolates himself from his family which allows him to fall into obsession and ultimately leads to creating the monster. After the creation of the monster, Victor's failure to be a father figure drives the entire plot of the novel. Shelley forces the reader to ask whether the story would have been a tragedy if Victor had taken responsibility for his creation--essentially his own child. Victor holds all the responsibility to raise his creation, as he has created in the absence of woman, which is an entirely different problem in the novel. At one point, the creature even says, "My creator viewed me as an abortion," (chapter 24, part 3) which reveals that even the creature itself knows that something is amiss. Yet, even though the creature recognizes that something is wrong with his paternal relationship to Victor, he cannot seem to right it himself and instead falls into violence. Perhaps, Shelley suggests, if Victor had taken his paternal responsibility seriously in regards to his creation, the lives of his loved ones would have been spared.
As to the second part of your question, dealing with Shelley's concern over correct fatherhood, it stems partly from the enlightenment idea of Tabula Rasa. When we are born, according to this view, we are blank slates which society and our families write upon. The influences our families have on us create what we will be ultimately. When Victor steps out of his creation's life, he is allowing the world to shape it entirely, and the world the creature encounters reacts to his hideous appearance with violence--thereby teaching him to live by violence. Additionally, Mary Shelley had only her father, William Godwin, since her mother died when she was less than a year old. Her father, however, responded by sending his children away to live with someone else--effectively abdicating his fatherly duties. Ultimately, he did provide Mary with an education which would not have normally been available to women in that day. As far as personal teaching, though, he was largely absent. Her novel explores a father-child relationship gone wrong and shows the way the world can corrupt the Tabula Rasa of the child in an absence of a father figure.