Parsing (as usually understood) is about grammar only, and the confusion bad grammar sometimes creates.

Most deceitful language from ads and pols is grammatically correct and, of course, easily comprehensible. That's what makes it work.

The most important course any student can take is what my alma mater called "practical reasoning."

Deduction. Induction. Close attention to the meanings of the words used. Identification of misleading arguments and appeals.

As an undergraduate I had a full semester of this. (It wasn't enough.) Every student had to learn composition, but "practical reasoning" was only an elective.