I've yet to see someone complain that software engineers don't build engines and are therefore bad at their jobs. Indeed, that'd be a silly argument.

Also, you've completely ignored my first point above. Even if we accept that teaching is the primary responsibility of a "Professor", it does not follow that this teaching manifests primarily as classroom teaching. Advising is teaching, and is the primary form of teaching undertaken by professors at certain research-intensive universities.

Incidentally, there are job titles that describe classroom teachers at research universities -- "instructor" or "teaching professor". The author of this post was not an "instructor" or a "teaching professor". He was an assistant and then associate professor. Classroom teaching was not a majority component of his job.

Luckily for every software engineer out there, historical cruft in the names of job titles is a bad criteria for evaluating job performance.