Apparently they had a lot of problems and were supressed in a lot of countries. Even certain Popes suppressed them? Why is that?
This is strictly my understanding, but the Jesuits are perceived as being quite liberal, so more conservative Catholics didn’t always agree with their beliefs. My understanding is that even St. Pope John Paul II had issues with them, but it was worked out during his papacy. I think to a point I can understand it, as I lean more on the conservative side myself, and there are things the current Pope does that I sometimes don’t understand.
I don’t think it had anything to do with liberalism. That is more of a 20th/21st Century thing with the Jesuits. I don’t know all the historic details off hand, but I think it had more to do with power and politics of the time. Many countries expelled them mostly because they were so influential, especially in the mission territories of the New World, and this eventually convinced the Pope to suppress the order. There’s more to it, and I’m rusty, but I’m pretty sure it had more do with 18th Century politics and power than any sort of theological disagreements.