A comprehensive answer would far exceed the space available. Countless individuals and groups have countless quarrels with the Church over countless grievances, real or imaginary. Let me speak of just one group—America’s secular establishment—which is of particular relevance in the present context.
By “secular establishment,” I mean the cluster of people who dominate America’s secular culture and its institutions—the great universities, the national media, the big foundations and think tanks, and now of course the White House.
It’s fair to say these people for the most part subscribe to a world view in which traditional religion does not play a large role. They are not just “secular” but secularists—secular ideologues—for whom a certain coolness (I use as neutral a word as possible) toward the Catholic Church comes naturally.
They also share a particular approach to resolving ethical questions. Pope Benedict famously spoke of the “dictatorship of relativism,” and that is one way to express it. Another way, highlighting the sources of antipathy to the Church, is along the following lines.
The Catholic Church adheres to an ethic of substantive human purposes—things like life, truth, and justice—that establish the parameters of ethically acceptable choices and behavior. To do the right thing is to act within these boundaries; to do what is wrong is to act outside them.
The secularist mindset, by contrast, favors a libertarian ethic of process and procedure—values like democracy, equal opportunity, and that epitome of the process ethic, the “right to choose.” To be sure, most people rightly live by a mix of values of both kinds—partly substantive, partly procedural—but the differences in emphasis are real and often extremely important.