When learning any subject, it's useful to divide it up into items you should memorize, items you should access via reference materials and items you should deduce.
You should memorize the subject's foundational items. For instance, it's really hard to do even the simplest math without knowing the digits by heart.
You really need to boil down the "memorization list" to as few items as possible, because it's difficult (and time consuming) to cram many items into your brain. You’re RIGHT to complain about the teacher who forces you to memorize endless facts. But when a teacher tells you that you need to memorize a short list of crucial data, you really SHOULD memorize it before you move on.
For second-order info, you're best off working with reference materials. (I.e. memorize the primary colors; look up the secondary colors that you get when you mix them.)
Finally, there are many items that need to be deduced, because they can't be codified into memorized (or referenced) facts. When I program computers, I generally hold the common commands in my brain; I augment my brain with reference materials, which are for obscure commands. But I must DEDUCE a way to cobble these commands together into a program. No book (or brain) can hold every possible program.
It's almost impossible to deduce without first mastering the foundation. In other words, before you'll be able to do any original work -- deductions -- you first have to memorize and learn how to use references. You can't make cake without ingredients.
I found this to be true when I learned Photoshop, a famously difficult program. It’s complex for many reasons, but initially it’s complex because it contains so many tools and options. After spending six months with the program, I had pretty much learned how to use all its tools. But I would be flabbergasted each time I read a tutorial about doing performing a complex operation, like color-correcting an image. What really confused me was that though I understood each individual step of the tutorial, I couldn’t understand how the writer had cobbled all those steps together into a meaningful whole.
My problem was that though I understood all the tools, my grasp on them was shaky. I wasn’t yet feeling them in my bones. One I really memorized them -- once I knew them so well that they popped into my mind without any effort (I got to the point where I could "manipulate" them in my mind, without even starting up the program) -- they magically became simple blocks with which I could build complex structures. This process took about a year.
Obviously, people will disagree over which items should be memorized, which should be referenced and which should be deduced. But agreeing on these categories gives us a good starting point for discussion.
Unfortunately, when you attempt to learn a new subject, you will be clueless as to how to categorize its items. Which should you memorize? What reference books should you buy? Once you master the foundations, what sorts of structures can you build from them? This is where you need help from an expert. A good teacher will point you towards the items you should memorize, the references you should use, and the items you need to deduce. He will try to minimize the number of memorized items, but, such as they are, he will strongly urge that you DO memorized them.
Alas, most teachers (in my experience) don't think this through. They just throw items at you willy-nilly, asking you to memorize some (and not others) almost at random. Well, not really at random (though it may seem that way). Alas, teaching tends to be based on ritual and tradition. So if your teacher tells you to memorize something, it's probably because that's just the way his subject is traditionally taught.
SOME memorization is vital, but teachers should remember that memorizing is (for most of us) the least fun part of learning. It's also the most perplexing. We wonder why we're being asked to memorize a bunch of, seemingly, random facts. This problems is compounded by the fact that we must memorize before we can do anything fun or useful with the subject. (You have to memorize French grammar before you can speak French.)
It's vital that teachers remember to explain WHY they are asking us to memorize. And, when possible, they should give us breaks from memorization. Often, one needn't memorize all the core facts to do some useful or fun work. One can memorize some; then use those facts in context. Then one can memorize more -- adding new tools to an already useful belt. Once we feel the utility of the memorization, we'll be more willing and able to pursue it.
A simple example is language:
Memorize: all the letters, the rules of grammar, and a fairly large vocabulary of general-purpose words.
Look up (don't memorize): obscure words.
Deduce (build from memorized and looked up items): unique sentences.