First, let me say that I have no doubts that Classical Education works for some. There are some aspects on which I agree with it, but also some I don't like. However, my biggest reason for not really ever considering this method is simply that it would never work for MY kids.
What I like about it:
I like that it expects foreign languages at a young age. I think that too many people wait until Jr High or High School to start foreign languages. If a person is not already familiar with at least one foreign language by about puberty, they will have a much more difficult time in learning any other languages. This is proven. Now, I don't think that Latin, Ancient Greek, or other dead languages need to be started in preschool years, as some people do. Truly, I think that starting them on foreign languages before 5 or 6 should be for reasons such as living in a bilingual household, having family or close family friends that speak another language, or living in an area that is largely bilingual. Starting ASL at pretty much any age is also understandable, especially if the child is struggling or delayed verbally or if they will need ASL to communicate with someone close to them (such as family member, close family friend, their babysitter's child, etc.). However, the dead languages don't really have much use in the life of most 3 year olds. Therefore, I see no point in starting them on those languages prior to Kindergarten or 1st grade. Of course, this may be partially due to the fact that, when my kids learn a language, I expect them to be fluent in it - reading, writing, and speaking - which requires more in-depth study than simply learning vocabulary.
I like that it places a strong emphasis on History & Science. Many people don't really feel that both of those subjects are of equal import as Math & Language Arts.
I like that it expects History & Science topics to be covered more than once.
What I dislike about it:
I dislike the 4-year rotation for History & Science. I feel that it limits what can be covered in those subjects, doesn't allow for rabbit trails, and never truly allows real in-depth study of any specific topic, providing just an overview.
I dislike the emphasis on memorization, especially rote memorization. The Well-Trained Mind website actually says that children in the Grammar stage enjoy memorization & that the focus of those years should be on memorizing facts regardless of whether or not the child has any understanding of them. NO, NO, NO, NO! I can not say NO loud enough or enough times to a sentiment such as that!
Now, for a quick offshoot on my feelings regarding rote memorization. Memorization is the lowest form of thinking & learning. It should be used sparingly. Rote memorization is torture to a thinking human being. Rote memorization is sitting there with the Multiplication Table in front of you repeating over and over: 1 times 1 is 1, 1 times 2 is 2, 1 times 3 is 3, etc. Rote memorization is doing drills with flashcards to memorize the content. Rote memorization is NOT fun. Applying the concepts in order to play a game is not the same thing as Rote Memorization. Playing fun Math games, like Timez Attack, is not Rote Memorization. It is placing those facts into long-term memory while building speed & fluency through the application of the Mathematical concept. There is a huge difference. I would NEVER force rote memorization on my child. We use flashcards & do drills ONLY if they want to. I do not require them to memorize their Math facts before moving on to the next concept. My son is currently learning long division, and still plays multiplication games to build his speed & fluency with multiplication. He might not be able to spit out the answer to any random multiplication problem in 3 seconds or less, but he can multiply any positive, non fractional, numbers you can give him, often doing multi-digit multiplication in his head. In my opinion, that is much more important than being able to rattle off the entire multiplication tables due to hours of wasted time & energy of rote memorization. I don't pass judgment on others for using Rote Memorization. If that's how you want to do things, that's fine. However, I find Rote Memorization a complete waste of our time.
I dislike the fact that it doesn't feel that Art and Music are important enough to warrant yearly coverage.
I truly dislike its dependence on textbooks & workbooks.
I dislike that it assumes that visual learning is passive and therefore useless. Visual learning does not have to be passive, if it is used correctly.
I dislike the emphasis on reading the Classics. I am not saying that we should not expect our children to read the Classics. I simply disagree with anything that says that the Classics should make up all or most of what a child reads. Not all the Classics are good, and not all will appeal to everyone. I can find just as many grammatical errors in some Classics as I can in some recent books. I personally hated Jane Eyre. I don't care what anyone says about how much merit it has. I couldn't stop comparing it to the Twilight series. There is nothing wrong with reading modern works. There is nothing wrong with reading works that have no real merit, as long as you can discern that they have no real merit. The books our children read should not be limited in this way.
Probably my biggest dislike about this method, though, is the fact that so many (especially many of those using the Classical Method) assume that it is automatically more academically rigorous than EVERYTHING else.
Despite what I consider to be the cons of this method, I don't think it is a bad method of education. Each of us has our own expectations & ideals for education. This method simply doesn't meet mine. I feel it lacks the flexibility my family needs. It also wouldn't work for my kids due to the fact that their development is not on the same timetable this method uses.