My experience has taught me that attacks usually begin with the history, then with a misunderstanding of what the Church believes and teaches, then with angry comments about why the Church is so “obsessed” with the life issues and then a whole bunch of criticisms. These days, tragically, the Catholic clergy abuse scandal is thrown in somewhere. It has to be discussed – but honestly and accurately.
The rest of the punches thrown at the Catholic body? The Church was nasty to Galileo; the Church tried to convert Muslims, and the Crusades were horrible; Hitler was a Catholic and the pope was a Nazi; the Inquisition slaughtered millions of people; the Church is rich and does nothing for the poor; children were abused and the Vatican knew about it all and did nothing; celibacy leads to perversion; Catholics worship statues; Catholics believe the pope is infallible and can never do anything wrong; and so on and so on and so on.
It’s all nonsense. Yet nonsense that is given a veneer of credibility by thinking people who shape opinion. All this makes the Church unique in the twenty-first century as a victim institution. In almost every other area, we’ve matured as a people and a culture to the point where such crass generalizations and fundamentally flawed opinions would not make it past the alehouse door.
There are two reasons they are allowed to persist.
One is that the Church's enemies find them useful.
Two is that Catholics, particularly professional Catholics, don't stand up to challenge these beliefs.
They've swallowed up the ambient secular culture and undermining secularism might turn them into the, ahem, Taliban, and undermine their own theological agenda.