Well, notwithstanding the fact that most Lutheran families are Lutheran because their ancestors were and that dates back to the Reformation and has nothing to do with the Church of England, and many churches with “Reformed” in their name derive from Calvin, I do take your point – you do have the Episcopal > Methodist > Wesleyan > Holiness > Pentecostal sequence, with people stopping anywhere along that sequence.
But, at rock bottom, the understanding of the Anglican Communion is this: Like the Orthodox, the Church in the West was divided up into national churches supported by the crown in each nation: the Church of Sweden under the Swedish monarchs, the Church of France under the French monarchs, etc. All were united into the Catholic Church under the spiritual leadership of the Patriarch of Rome, AKA the Pope, but had their local church government run by a Primate, ordinarily an Archbishop, who worked with and for the Pope and the monarch as appropriate. (Naturally, there were some problems where authority overlapped, but we’re talking the everyday process.)
Throughout history, kings tended to make marriages that benefitted their realms, marrying the daughter or sister or niece of a neighbor monarch to tighten an alliance, marrying the heiress of a neighboring county or duchy to bring that under their rule, and so on. When such marriages violated the specifics of canon law, the Pope was pleased to grant dispensations; when there was a need to put away a wife and remarry owing to lack of interfertility, the Pope could be counted on to grant an annulment (not a divorce; an annulment is an official declaration that, contrary to appearances, what seemed to be a marriage really was not one, as in the apocryphal case of the guy who gets drunk and wakes up next to a strange woman who claims he married her the night before – there was no real intent to wed there).
Henry VII had arranged one of these marriages for his son Arthur, to Catherine the daughter of Ferdinand and Isabella of Spain (Ferdy, by the way, was one of those kings who married for dynastic reasons, Isabella being heiress in her own right of Castile, the large central region of Spain, while he was king of the smaller Kingdom of Aragon in the northeast). When Arthur died young, Catherine was married to the new heir, Henry. They had one daughter who lived, Mary, and a half dozen miscarriages. Eventually Henry decided that having married his brother’s widow (which was a violation of canon law from which the Pope had granted a dispensation) was actually a sin, and he was being punished for it by not fathering a male heir. Simultaneously, he developed the hots for Anne Boleyn, which was a second contributing factor in his request to the Pope to annul (not divorce) Catherine.
However, the Pope was, reasonably, in Rome, which was at this time occupied by the troops of Charles V, the Holy Roman Emperor, and coincidentally the nephew of Catherine. Charles did not want his beloved aunt put away, and the Pope, looking at the troops outside, was pleased to deny Henry his request for an annulment.
There was precedent in Germany and France for the local church to revoke the Pope’s authority over a given canon law issue and retain authority in the local Archbishop’s Court. Henry decided to resort to that, to have himself as monarch and defender of the faith (a title the Pope had given him for writing a treatise against Luther’s heresy) declared Head of the Church in England and deny the Pope’s authority to grant or deny annulments, just as the Kings of France and Holy Roman Emperors had done in the past.
As it happened, however, this was at the beginning of the Reformation, and the Church of England, which dates at least back to St. Augustine of Canterbury in the 500s AD, never negotiated for reunion with the Papacy as the previous instances of such rebellion had ended with. It remained a slightly-schismatic branch of the Catholic church for about 40 years, until a later Pope, influenced by Philip II of Spain who was making war on the first Queen Elizabeth, excommunicated her and her subjects. And that is more or less where things have stuck ever since. There have been “swervings” in Anglican theology more towards Protestantism and more towards Catholicism, but we’ve always maintained the status of a “bridge church” that is truly Reformed and truly Catholic in our beliefs.
