This is a great question. There are several reasons why the papacy did not favor the printing press.
First, the Catholic church can be viewed as a clerical church, whereas Protestantism can be viewed as a laity church. The Catholic church, in a sense did not want the people to read the Bible for themselves. The Catholic church wanted the priest to lead these things. Hence, the printing press had the potential to undercut this for the simple reason of the proliferation of book. Protestants had a different view. They believed in the perspicuity of scripture and wanted people to have it in the vernacular.
Second, Protestants did a great job, a far better job than Catholics, in using the printing press to spread their ideas. For example, people like Martin Luther were extremely prolific and they directly challenged the Catholic church and even swayed the public with reading their tracts. This made the Catholic church nervous. This fact also made the Catholic church distrustful of the printing press.