The eighteenth-century expulsions of the Jesuits from various countries and subsequent suppression of the Jesuits overall were the result of a combo of unlucky factors -- a general climate of political change certainly didn't help, but there were reasons to single out the Jesuits for expulsion rather than another religious order. The Society of Jesus had become large enough and economically profitable enough to be conspicuous; Jesuits had become visibly involved in politics and education in a way that made them wildly unpopular. Anti-Jesuit sentiments in the popular press had reached critical mass, presenting Jesuits as inherently treacherous and interfering, and individual Jesuits had been implicated in enough political scandals that the idea of a wealthy and influential Jesuit order had begun to sound hazardous to a monarch's health. This cocktail of factors united a number of groups who otherwise might not have gotten along too well (progressive Enlightenment types, anti-clerical types, ardent supporters of monarchy, competing sects of Catholicism, individuals with financial stakes in the New World) and gave them a common cause -- opposing the Society of Jesus.

The expulsion of the Jesuits from Portugal (1759) and Spain (1767) makes for a good case-study in the causes of the suppression, and these two set a pattern for how expulsion could be achieved in other countries -- I don't think it was purely a case of Joseph I of Portugal and Charles III of Spain popularizing a how-to protocol for "here's how to expel your Jesuits and maintain plausible deniability when you scoop up their land holdings", because the economic and social threat the Society of Jesus presented to their opponents was seen as very real; the Jesuits weren't total scapegoats in all this. But the immediate impetus for the Portuguese expulsion (armed colonial conflict in Paraguay and the scandal of an attempted regicide) at least popularized the idea that the benefits of permitting the Jesuits to remain didn't outweigh the risks of Jesuit political interference. Once the Society was ejected from Portugal and Spain, its traditional seat of influence since its inception, it lost its foothold in the colonies associated with those nations; once it lost its position in France and Italy, the death-knell had pretty much sounded for it, and expulsion from any remaining territories was only a matter of time. Jesuits were forced out of these countries on short notice (with no chance to liquidate or relocate their property holdings) and priests were escorted back to the Papal States with little fanfare. (Weirdly enough, one of the few places where the expulsion of Jesuits was resisted or at least delayed by the ruling monarch was Russia under Catherine the Great-- many Jesuits who had been expelled from their home countries found refuge and employment there during their effective exile.) All of this was capped off by the Papal suppression of the order in 1773 -- this was the final blow to the old Society, the loss of its traditional closeness with the Pope that had sustained it for so long. The era of Jesuit influence had run its course since the 16th century, and the features of the Society that had once seemed new and exciting now seemed like outmoded relics of the old world.