What are the Renaissance and Reformation greatest challenge to the established authority of the Catholic Church. What aspects of Renaissance and Reformation are contributing most significantly to undermining the authority of the Catholic Church ?
The Protestant Reformation
In the Go-Go days of the Middle Ages, the Church was the most powerful institution in Europe, and the Pope was very close to being an emperor. The Church's declining influence--and the growth of Protestantism in Germany and England-- was one of the defining elements of the end of the Middle Ages and the start of the Renaissance.
At the height of its powers, the Church called for four Crusades against the Muslim world and got a very enthusiastic response (although technically, they lost three of these and the one that they won resulted in an anemic and short-lived Crusader Kingdom headquartered in Jerusalem). By the time Martin Luther nailed his Ninety-Five Theses to the church door in 1517, the Pope had actually called for two more Crusades that hardly anybody showed up for.
While the Church remained a very powerful institution, they lost their monopoly on European theology. Almost all of England converted to Protestantism, Bibles were being printed in vernacular languages so ordinary people could read them and see what they actually said, church officials were being defenestrated through high windows in Prague, Copernicus and Galileo demonstrated that at least a couple of Bible verses were not literally true, etc.
The Reformation encouraged people to think and decide for themselves instead of accepting the authority of the Catholic Church.
The power of the Catholic Church was partially based on the Churches teaching that the Catholic Church was capable of inerrancy. The Pope was granted the authority to speak from the seat of Saint Peter to speak inerrantly for God.
The Protestant Reformation undermined the power of the Church by stating that the Bible was the ultimate authority over the authority of the Catholic Church. The Protestant Reformation encouraged the people to read the Bible for themselves, and decide what the truth was. This ability of people to decide for themselves undermined the authority of the Catholic Church.