That two numbers applied to division don’t form a term?

Now you're getting it! Correct, they don't. They form an expression. Terms are separated by operators, and joined by grouping symbols. Expressions are made up of terms and operators (since, you know, operators separate terms). I told you way back in the beginning that 1÷2 is 2 terms, and ½ is 1 term. Getting back to the original question, 2(2+2) is 1 term and 2x(2+2) is 2 terms.

you find yourself an authority that you trust

Which time that I mentioned textbooks, historical Maths documents, and proofs did you miss?

university professor

University professors don't teach order of operations - high school teachers do. That's like saying "Ask the English teacher about Maths".

If you want to continue this

Why would I want to when you ignore Maths textbooks and proofs? See my first comment in this post that you've finally got the difference now. See ya.