Science Lesson — Even assuming time travel were possible, a person becoming his or her own ancestor would be very unlikely, although not impossible.
For sexual reproduction to work, a person's chromosomes are split into two sets. In women, these are stored in eggs; in men, sperm. The two halves are joined during conception to create the genetic template for the new individual.
For someone to become their own ancestor, the exact same set of chromosomes must be passed down through the generations. In Fry's case, for example, the sperm that conceived his father would have contained all the genes Fry already received from his father. Then, when Fry's father mated with Fry's mother, the sperm that conceived Fry would have had the identical genetic makeup as the one that conceived Fry's father. The odds against this are staggering. And for each generation removed, it becomes more unlikely, because the exact same genetic code must be passed down through the generations or the ultimate result, in this case Fry, will not be genetically identical to himself, creating a paradox. But since Fry is his own grandfather, his sperm beat the odds twice.
Imagine if Fry went back to the middle ages or Roman times to conceive an ancient ancestor. The same sperm variation would have to be passed down 100 times, and that just doesn't happen, considering the complexity of our genetic material.