We can take the noun "can" and form an unlimited number of coherent and sensible noun phrases, including: a big can, a blue can, a heavy can, an empty can, a tin can, a coffee can, an oil can, a trash can. Just as you've surely noticed, the words big, blue, heavy, empty, tin, coffee, oil and trash all do the same job. They all modify the noun "can". In high school, I was taught to label all these noun-modifying words as adjectives. If we only want to look at the work that these words do for or on the word "can", that's fine.
But, if we want to look at the jobs that can be done for or on those words, we find that there is a significant difference. There's at least one kind of word that can modify adjectives. In high school, I was taught to label all of those words as adverbs. One example of such an adverb is the word "very".
These phrases work: a very big can, a very blue can, a very heavy can, a very empty can. These phrases fail: a very tin can, a very coffee can, a very oil can, a very trash can. Big, blue, heavy and empty seem to be one type of word. Tin, coffee, oil and trash seem to be another type of word.
There is more than one way to address this difference. We could consider "trash can" to be just one word (a compound word) that is just one part of speech (a noun) but consider "empty can" to be a phrase with two separate words (empty and can) and two separate parts of speech (adjective and noun). That sounds like the approach that your German English teacher takes. Alternately, we could consider tin, coffee, oil, trash and can to all be nouns. All of them (can included) are used to modify other nouns, and there's nothing special about the way these words combine. Given the noun "crusher", we can talk about a can crusher as easily as a tin can, and even talk about a tin can crusher if we so wish. I used to have a very blue tin can crusher, but I threw it in the trash can.
Whatever system of labels you prefer, it is more useful to use a system that describes both what the words can do and what can be done to them. Labelling the "trash" of "trash can" as simply an adjective ignores the fact that "a very trash can" is not a coherent and sensible noun phrase.