First, we must note that any answer to this question has to be somewhat speculative. We cannot go back in time and interview Pope Urban to figure out why he was so worried about Galileo. Instead, we can only make educated guesses. One possible answer is that the Catholic Church was under a lot of pressure at the time and did not want to deal with further challenges to its authority.
By the time that Galileo got in trouble with the Church, the Church’s power had been in decline. Martin Luther had started the Protestant Reformation about 100 years before and the Church had lost its monopoly on religion in Western Europe. The Church was also in the midst of the Counter-Reformation, in which it was trying to win back its power and prestige.
In such an environment, the Church was not going to be very tolerant of public dissent. This is, at least arguably, why Galileo got in trouble. The Church taught that the Earth was the center of the universe and that the Sun revolved around it. By arguing for a heliocentric (Sun-centered) solar system, Galileo was arguing that the Church was wrong. This was dangerous for the Church because it would erode the Church’s authority. In an attempt to prevent its authority from being eroded, the Church objected strongly to Galileo’s theories.