Guy offers a cause for the start of Henry's troubles: one of his blood factors was probably in conflict with Katherine of Aragon's and later Ann Boleyn's. (He doesn't specify, but perhaps he means the Rh factor.) This would explain why, untreated, both queens were "lucky" to be able to bear one child with him. It was just their misfortune that those children happened to female.
It doesn't need to be belabored that Henry's perspective that a woman couldn't rule was sexist. In his defense, there was little precedent for it at the time, and at least in this treatment his primary concern seems to be what will become of the monarchy after the queen marries. It seemed impossible for Henry to imagine that a queen would be strong enough to dominate her husband, and upon reflection, given the times it seems unlikely that anyone would get that close to power and not be tempted to consolidate it. At the worst, the new king would dominate his wife; at the least, a marriage would run the risk of splitting the government into factions (and certainly this is what happened to Mary when she was married to Philip). Elizabeth, who ultimately decided it would be imprudent to marry, also noted that marriage to someone of her rank created an equal number of vulnerabilities that marriage to a commoner would.
While this does cover some of the highlights of the biographies- Ann Boleyn may very well have been an evil stepmother; Mary's devotion to her Catholic faith may have been as much an act of defiance as it was genuine piety; Edward was closest to Elizabeth of all of his siblings; their half-brother Henry Fitzroy entered into a marriage agreeing not to consummate it; and Elizabeth learned her survival skills at an early age, beginning with the scandal between Thomas Seymour and herself- what it goes into greater detail about is the way their educations and households were organized. In all cases, by the time the royal children were four months old, their households were established away from their parents. However, both Katherine and Ann went out of their way to see their daughters beyond what was proscribed by royal protocol. (Jane Seymour, Edward's mother, never had the chance as she died shortly after his birth.) While Henry wanted to see his daughters educated, he did not see any reason for them to be educated in a way that would prepare them for rule. However, it seems that both princesses applied themselves well- better, perhaps, than their brothers.
Interestingly, Guy argues here that both Mary and Elizabeth were far more merciful than they have been recorded elsewhere, particularly in the cases of Jane Grey and Mary Queen of Scots, respectively. Mary- later known as Bloody Mary- was inclined to spare Grey's life out of loyalty to her mother, but was moved to execute her after the first of many Protestant rebellions. Elizabeth, while seeing the need to imprison Mary (of Scotland), was reluctantly talked into executing her but apparently changed her mind at the last minute. Her counselors, however, had her executed anyway. Regardless of her personal feelings toward Mary, Elizabeth was devastated by this decision because it set a precedent for the weakening of the legal monarch of a country, and she was wise enough to know that English rulers would not be spared. (And in the cases of Charles I and James II, she would be proven correct.)
The tragedy of Henry's family is that while he was obsessed with continuing the dynasty, his actions and pronouncements made it impossible for his children to do so. While England became a stronger country under Elizabeth, her death ended the Tudor line. James, Mary's Scottish son, was the grandson of Henry's sister Margaret, but thereafter the rulers of England would be Stuarts, not Tudors.
Recommended for those interested in English history.