The Second Lateran Council of 1139, presided over by Pope Innocent II, is generally cited as including a ban on crossbows but the actual text suggests that a more general ban on both bows and crossbows was intended. It also only bans the use of the weapons against other Christians, using them on Crusade was perfectly allowed.

As to the why that lies outside of my expertise, unfortunately. While I've heard claims that it was out of a fear of a peasant with a crossbow shooting a noble knight to death, that is an idea based exclusively on speculation that doesn't seem plausible to me. It's far more likely the declaration fit within the overall attempt by the Catholic Church to regulate secular military actions in an attempt to limit inter-Christian warfare. Other examples of this movement are the Peace and Truce of God of a few centuries earlier and, in part at least, the Crusades acting as a force to direct Christian aggression to areas beyond Europe.

A similar question came up some months ago, and the responses to that may be of interest to you as well. Link