The crusades started because the Byzantine emperor asked the pope for some Western knights to help him fight the Turks. The Crusaders did help the Byzantine Empire regain some of their recently-lost territories...but unfortunately the "Franks" and the Greeks tended not to get along. Odo of Deuil's account of the Second Crusade shows a lot of mutual dislike already by then, more than 50 years before the Fourth Crusade.
The Fourth Crusade was a disaster in many ways but the diversion to Constantinople happened because an exiled member of the imperial family begged the Crusaders to help him restore his deposed father to power.
Plus, the doge of Venice had a score to settle.