A badly stated issue calls for false or extreme solutions. It is important, therefore, to correct the impression that the issue in American education today is between classicism and progressivism.It goes on and if you are interested in the subject it's well worth reading the whole quote at the Quiddity blog.
I think that today, as opposed to when Adler wrote, the issue is somewhat different because sterile classicism disappeared thoroughly into the woodwork to be replaced by a kind of Back to Basics pragmatism. I liked his mention though of falsely framing the debate. It's something to think of when you are embroiled in some discussion where you find yourself being put into a sort of polarized position. Maybe you are dealing with a false dichotomy and if you restated the issue you could come up with something more durable and defensible. In other words, something that approaches truth, maybe?
There's a Greek word "stasis" which originally meant "strife" or "stopping point" and has been used in the study of rhetoric. It has to do with judicial procedure but seems able to be transferred to other types of deliberations.
When you are boggled in some argument you can consider:
Fact -- What is the subject we are discussing? Do we both frame it the same way or are we talking about different things?
Definitions -- what do the terms mean? Does everyone define the same words the same way? Many, many disagreements are complicated by semantic confusion.
Quality -- this has to do with rights -- maybe since lots of discussions are based on underlying principles, it's important to find out: What are the presuppositions or premises that people are starting from?
Jurisdiction -- Is this is the appropriate place or occasion for the debate? Are the proper people engaged in it (brings up authority issues, prudential issues, among others -- for example, my neighbor can't really tell me whether I should homeschool or not)
Thinking this through can help avoid those looping, unproductive arguments where no one really knows exactly what they are talking about and everyone is getting more and more frustrated. Even if it doesn't help the argument or discussion itself, it can help onlookers make a fair judgment. Especially having several teenagers in the house, I've found it useful in those tricky subjects to try to dig into those different aspects of it. Over time, one finds, the teenagers develop the habit of slowing down and checking their systems for themselves. But definitely it's a process.