"why, in 1179, did the cathedral school of notre-dame in paris start admitting nonclerical students? "

The correct answer to this open question is the following.

In 1179, the cathedral school of Notre-Dame in Paris started admitting nonclerical students because a papal decree ordered their admittance.

The monastic schools were the first kind of education centers created to teach and train catholic priests in Europe, during the Middle Ages. In these schools, like the cathedral school of Notre-Dame in Paris, monks studied the Bible and Theology. With the approval of the pope, many new nonclerical students attended this school due to the excellent education that was imparted.

council members were chosen randomly, and men could present laws for debate in assembly.