Elsewhere, among a group of high school math teachers, I encountered a discussion of the term 'cancel'. Most (>20) people in the discussion had very strong feelings about why the term should be eliminated. I searched among posts on this stack to find the word common used and its meaning seems well understood.
The objection the the word's use included the concern about errors that might result from dividing to cancel and thinking that zero results.
My response was that if a student's work reflects accurate use of subtracting from both sides, dividing properly when attempting to simplify, etc, that what the student calls it is far less important. I even suggested that it would be preferable to teach the proper name for what's occurring, e.g. 'The additive inverse property' but as long as the student is doing the math correctly, and typically, silently, that there's no harm in using a word that's less than a textbook definition.
(Given the use of the word here, over 100 posts, and no pushback that I saw when skimming over a dozen, I suspect I know the answer. I'm here for confirmation)