It could be argued that Victor Frankenstein is the "father" of the monster, since Victor crafts the monster out of scavenged body parts and uses his study of the occult to bring his creation to life. The monster did not ask to "be born" or to live just as children don't ask to be born of their parents. Most parents would likely agree that once a child is born, it is the responsibility of the parents to raise, care for, protect, and guide the child until the child is able to care for oneself and live as a productive adult. You don't have to dig too far into research in the social sciences to encounter many examples of how a child's development is negatively impacted by being abandoned or neglected by either parent, though the effects of a father abandoning/neglecting a son are a special subset both in literature and in psychology/sociology.
If you agree that a father should be both a role model for his children and also be responsible for guiding them towards a moral compass of what constitutes right versus wrong, then consider the significance of Victor's reaction to the creation of his monster. When he sees that his experiment was successful, he grows instantly repulsed and rejects and abandons the monster to the world. When we later meet the monster again (after it has murdered members of Victor's family), we learn that it was not born evil but rather as it attempted to learn the ways of the world and to find friends and community, the monster turned bitter after experiencing rejection, fear, violence, and loneliness. The monster comes to hate Victor for bringing him into the world and not sticking around to help him navigate all the pitfalls of life. The monster was not born a monster, but rather its experiences of abuse and neglect turned it monstrous. Of course, Victor's failures as a "father" come back to haunt him as the monster continues to systematically murder Victor's loved ones.
The second part of this question leads a reader to think that perhaps Mary Shelley felt abandoned or unsupported by her own father, the philosopher William Godwin. Shelley's mother (the feminist Mary Wollstonecraft) died shortly after Shelley's birth, and Shelley reportedly didn't get along with her stepmother. Shelley's adult life was also riddled with tragedy, which may have factored into the "failed father" theme. Her husband, the poet Percy Bysshe Shelley, drowned during a sailing trip, leaving their then 3-year old son without a father for the rest of his upbringing.