Uh, Eliezer, when you were 9, had you seen a wave? Did you have a sense that a wave was different in several ways from other kinds of things, even from other kinds of fluid behaviors -- different from a current, say?
Now, when you were 9, had you seen an arglebargle? Did you have a sense of how arglebargles differed from other things? (If so, how?)
And are there ways in which the characteristics you did recognize in waves, when you were 9, also do in fact apply to light? On the other hand, are there ways in which the characteristics you recognize in arglebargles apply to light?
I would venture to say that you did learn something meaningful by repeating your teacher's explanation that light is "made of waves". You are overly discounting what counts as experimental evidence of the real-world phenomena which words refer to. You had a lot of experimental evidence of waves at age 9. You'd seen them, for a start. When your teacher told you that light is made of waves, he was helping you to understand something about light by explaining it in terms of something you had real-world experience of.
Similarly, when my 3-year-old asks whether stars are burning but planets are not, I don't tell him that actually stars aren't "burning" as such. I say yes, and what he said counts as learning, not "guessing my passwords" -- even though he doesn't fully understand yet what I would understand by the word "burning".