I don't understand the "memorize the pathways" style of teaching.

I'm not one of those people who says "Why memorize anything when you can look it up?" That doesn't generally work because (1) you need to know that a fact exists at all before you can look it up, (2) a lot of problem-solving is done by your subconscious, which of course can't look up anything, and (3) often you can't see the big picture until you have learned enough of the pieces, even though learning the pieces seems like arbitrary memorization while you still don't know enough of them.

However, I still don't see any point in memorizing lists of arbitrary alphanumerical protein names. Knowing the pathway's purpose, inputs and outputs, and any key intermediates is sufficient. I can't think of any scenario where a pathway isn't the focus of your research but being able to recall the names of all the enzymes and the order in which they act (as opposed to looking them up) is useful in practice.

(But maybe I'm the one who is ignorant of the practical applications of that knowledge... All I can say is that there has been no need for it during the course of my career so far.)