Why do we say "he is average height" and not he has average height". don't we use have for a noun and is for an adjective?

Answer 1

No, the adjective has nothing to do with it. He is the subject of this sentence. He is singular, so the verb must be singular. Is or has are both singular, so both are correct. In this instance we don't usually say someone "has" a certain height, we say is "average height" or "five feet nine inches". Has usually means an object, not a state of being, as in "He has five dollars," or "He has a wedding ring." We might say, "He has a wide wedding ring." The adjective has nothing to do with verb tense or case.

Answer 2

Errors will occur if you keep that "is" and continue the description with words that need "has" -- here's an example, straight from some of my students' writing in class:

Error: He is average height, red hair, blue eyes, and black clothes.

Fixed: He is average in height and has red hair, blue eyes, and black clothes.

It's not an easy concept, but ... it's English! And we all know English is not the easiest language to learn!