1713 was the middle-late period of the Protestant reformation. The Methodists were just breaking off from the Anglicans who had broken off from the Catholics. Lutheranism was strong as were the Calvinist churches. The early 1700's was also the beginning of the age of enlightenment which stressed reason and individualism.
The short answer is that all of the above combined to create an atmosphere where people were able to buy books freely, including the Bible, and draw their own conclusions. The Church's reaction at times was that Scripture should be left to the professionals, going so far as to discourage reading of scripture among the laity.
Catholics don't like to hear that this actually took place and bringing it up usually results in many angry rebuttals, quotes to the contrary and demands for proof. Unigenitus is one such proof. I have taken much flak for stating as much but the truth is the truth. The Church reacted, sometimes violently, against the Reformation, including discouraging private reading of scripture at times. People were reading scripture on their own and coming up with some pretty whacky ideas because they didn't understand the context of the passages. One such idea led to civil unrest in an area of France and the Bible was temporarily put on the index of forbidden books until the unrest subsided.
This is what you are seeing in Unigenitus. It was a product of its own time and written for its own time. It has to be read in the context of what was happening when it was written. The points cited were specific rebuttals to specific challenges against Church authority and the teaching office of the Church from the Protestant Churches at the time, many of which were quite powerful and growing.
The Second Vatican Council was, in many ways, a reversal of the defensive mindset of the Church in reaction to the Protestant Reformation. Instead of being defensive against an increasingly educated population, the Church opened up it's teaching and freely shared the Good News. Hence the term "Throw open the windows."
Unfortunately the defensive mindset still exists today. I invited a couple to join my Bible study and the gentleman replied, "I would never go to a Bible study unless it was run by a priest." It didn't matter to him that it was the widely accepted Jeff Cavins/Great Adventure series.