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I’d argue that Jesuit priests, despite being educated in highly religious schools, tend to be the more liberal branch of Catholicism due to their emphasis on logic and analysis.

I'd say it has more to do with their proletariat recruitment and lifestyle, but sure. Logic and analysis definitely have their role.

What I’m saying is that a good education is one that emphasizes critical thinking

Critical thinking is an engine, but you need the initial conditions to fuel it. Thomas Aquinas and Isaac Newton were both profound critical thinkers, but they came to remarkably different realizations over their lifetimes. We have critical thinkers who can't agree on shit all the time, and not just in the gulf between religion and science. Go into the realm of particle physics and you'll have people sharply divided on the fundamental nature of the universe despite enjoying ample expertise in their areas of study.

Go into public policy and you'll find the same divides. Critical thinking still needs a moral basis. Otherwise, you're just a paperclip maximizing engine, logically and emotionlessly determining the most efficient way to turn the whole world into consumer widgets.

There’s a scene in The West Wing where Sam Seaborn (Rob Lowe) is talking to, I think, Ainsley Hayes (Emily Procter). As I remember it, there was a paper arguing a conservative viewpoint on something, and Sam reveals that he wrote the paper as part of a debate exercise. I always thought that was the epitome of a good education: being able to switch your viewpoint and really understand the other side’s argument to the point where you can win a debate arguing for something you oppose.

Part of the joke of West Wing is that Rob Lowe is playing a conservative in a liberal administration. They all kinda are. That's Aaron Sorkin's brand of politics. Do conservatism from the left. So of course you've got Seaborn writing a paper from a conservative perspective and demonstrating a competency in conservative thinking and then having a conversation with another conservative about what Real Conservatism Really Means. These are two conservatives talking to each other about a shared ideological framework.

Go back and look at what the ostensibly liberal President of an ostensibly liberal party actually accomplishes while in office and you're going to find - Budget Cuts, Foreign Wars, and Privatization of Education and Social Security. Basically the Bush Administration's agenda for the second term in office.

A good education will force people to debate a viewpoint they disagree with

Show me the Aaron Sorkin character who credibly and sincerely makes an argument in favor of the Cuban Revolution. The closest they come is "Ninety Miles Away" and its not exactly flattering to Castro.