Note: I should clarify that my earlier comment ('that's false') referred to MCs latest entry in the Cutest Putdown contest--'personal interpretation.' That's a false charge against the reformed churches for sure.
Anglicans are not among the "Reformed churches" neither is Lutheranism. But the point is that Martin Luther pursued his own private interpretations and refused to retract any of them when he was challenged. His reply was, according to a disputed Lutheran Tradition, "
Here I stand (meaning on his interpretations of holy scripture)
I can do no other". A more accurate tradition about his words at the diet of Worms is this "
Unless I am convinced by Scripture and plain reason - I do not accept the authority of the popes and councils, for they have contradicted each other - my conscience is captive to the Word of God. I cannot and I will not recant anything for to go against conscience is neither right nor safe. God help me. Amen."
Martin Luther apparently felt bound in conscience to follow what he believed to be the meaning and hence the teaching of the holy scriptures. In consequence he eventually became the founding father of a group of churches that to this day bear his surname as a part of their names.
But if Martin Luther's alleged statement at the diet of Worms is correct and he refused to recant on the authority of popes and councils because they contradicted one another then how could his conscience be bound by the holy scriptures because they too contain contradictions that are numerous, too numerous to list here, why would his conscience rely on holy scripture and be bound by it when in fact holy scripture both says "no man as seen God at any time" and also relates the seeing of God by Abram, Moses, various prophets, Jacob, Adam, Eve? And when the holy scriptures contain the command "you shall not kill" and then relates numerous stories where God allegedly orders human being to kill? And killing is not the limit. Genocide is allegedly commanded by God and God himself destroys the whole of humanity with the sole exception of eight people who were either in Noah's family or were married to members of his family.
Now I know that apologists have explanations for these things some of which are credible and some which are not. So it seems that Martin Luther's conscience may have been bound by a subset of holy scriptural data, a subset that contained doctrines that he liked such as salvation by faith alone and the right of individuals to read and interpret holy scripture for themselves as well as the right of individuals or at least churches to decide what is and is not acceptable as holy scripture. And Martin Luther's followers and successors were not content with their own conscience driven right to believe according to their interpretation of the holy scriptures they were also keen to deny that right to minorities within their lands such as the Anabaptists who they persecuted as mercilessly as any Catholic and more so in some places.
What makes me reject Martin Luther's approach is not only the obvious subjectivity of it but also the obvious extension of it to other people such as John Calvin and Ulrich Zwingly as well as Henry VIII and Edward VI and Elizabeth I of England. These people did not agree on the way holy scripture was to be interpreted. They were at various times mortal enemies at least in part because of their differing interpretations. And after these came the Puritans in England who eventually executed their king (Charles I) and established a religious "commonwealth" where conformity to Puritan doctrines was obligatory upon pain of serious punishment and even death. Groups such as Baptists arose during these times and were persecuted by the Puritans and by the Anglicans when the Anglicans were in the ascendency. Each having their own private interpretation or if not their own then one from a leader who had his (usually a man) own private interpretation that became the foundation of a new denomination.
The process of leaders forming a "conscience driven private interpretation" which soon became the foundation of a denomination continues to this day. Though nowadays the matters over which division into new denominations arises has moved on into "end times" speculations, adventism, which days to keep or not keep. Many denominations grew out of well intentioned enthusiasm during the "great awakening", Methodism was born out of those times. Later came a "second great awakening" in the USA which led to still more differences and eventually some new denominations or sub-groups within larger denominations.
So even though John Calvin did not have any such pithy remark as is attributed, by some, to Martin Luther at the diet of Worms he did have a book and that book's doctrines became foundational for the birth of several of what are now referred to as "Reformed churches" and Presbyterian churches.
Thus personal interpretation was truly a major factor in the creation of Protestantism and the various denominations of Protestantism as well as Anglicanism and the later development of Pruitanism, Baptist churches, Methodists, and later still Pentecostal churches.
"Private interpretation" is only a "put down" for those who want to attribute something else as the impetus for the creation of their denomination - perhaps the leading of the Holy Spirit, a vision, the careful and well reasoned deliberation of bodies of allegedly godly men on the meaning of the sacred scriptures, or perhaps something else.