The Anglican Church is generally regarded to be more in line with the Catholic Church than with the Protestant Movement. It largely retains the Catholic structure, beliefs, and rituals. Consider it to be, for lack of better words, "England's Catholic Church." The Protestant Movement was an extension of Martin Luther's bold posting of the 95 Theses in 1517 in Wittenberg, which was the beginning of the Reformation. The proponents of the Protestant Movement truly wanted to reform the errors and injustices that they felt that had crept into the Catholic Church over the centuries. Some churches in this category are Lutheran, Baptist, and Methodist. Some felt that the Reformation didn't quite go far enough in its correction of errors ; therefore, in the 1800s, they began a movement which theologians generally regard as the Restoration Movement. These groups intensely focused on the Bible to see how things operated in the early New Testament churches, and sought to pattern themselves after those churches. These churches, including the Christian Church, and the Churches of Christ, are generally not "high-church," but "low-church," in which more importance is given to every member, every person has a part. This is in line with the Apostles teaching that every believer is a priest, only having to go through Jesus Christ, the high priest, in order to talk the Father (God). This is in stark contrast to the Catholic and Jewish (and others) practice of a believer's having to go through a priest to talk to God and to be forgiven of sin.
Sorry, I suppose I got carried away in attempting to give you a very basic overview of the Catholic-Christian Churches since 1517. In a nutshell, the Reformation and Restoration Movements
sought to restore the importance to every member which he/she originally had in the days of the early church before governmental beauracracy drastically changed the church structure and largely stripped the "layperson" of their individual freedoms in Christ, such as ministering to others and praying directly to God for forgiveness. By the way, based on what you believed to be the history of the Anglican church, your logic was sound.

It was the facts upon which that logic was based that was misguided.
