Classical learning is called "classical" because future leaders have been trained in its methods for centuries. In fact, some parts of the classical curriculum have been around for millennia.
Classical learning follows a particular pattern called the Trivium -- which consists of grammar, dialectic, and rhetoric. The students learn the grammar of each subject (that subject's "particulars"). They then learn dialectic, or the relationships of these particulars to one another, and then go on to learn rhetoric. That is, they learn how to express what they have gained in an effective and coherent fashion. The purpose of following this pattern is not to teach the student everything there is to know, but rather to establish in the student a habit of mind which instinctively knows how to learn new material when the formal schooling process is only a faint memory. The student is not so much taught what to think, he is shown how to think.
As Dorothy Sayers, author of the "Lord Wimsy" mysteries and a friend of C.S. Lewis and J.R.R. Tolkien, points out in her famous essay, "The Lost Tools of Learning," the three stages of the Trivium match the developmental stages of growing children quite nicely. The very great value of this method is that it provides a rigorous education suited to basic human nature and tested over centuries, rather than one developed from the theories of educational faddists.
Another significant part of the value of classical instruction is that it teaches students the rigors of logical analysis. Our society abounds in buncombe; we desperately need to train people to recognize it, so that someone might take it away. In short, we need more epistemological garbage men. This requires training in logic and the apologetics of Christian worldview thinking. Classical education supplies this in a way not seen elsewhere.
Third, the student learns that our culture and civilization is an outgrowth of the classical, medieval, and reformation world. Modern students must learn that our culture was not purchased for them by their parents at the mall. As C.S. Lewis pointed out, by reading old books the student is protected against some of the sillier mistakes of modernity.
Should every child master Latin, logic, and literature? No. A classical education is not suitable or desirable for everyone. When the apostle Paul teaches about the functioning of the body, he insists that not everyone should be a teacher. At the same time, he insists that teaching is most necessary. In other words, some people must learn to teach and lead (at this, classical education excels), but it is wrong-headed to insist that everyone must go to the amount of effort required of leaders.
The task ahead of us is nothing less than the recovery of western culture. For this task, we do not all need a classical education. However, at least some of our children must receive such an education, for the good of all of us. Classical learning is ideally suited for the training of cultural leaders, and that is what we so desperately need.