Assuming your primary goal is to communicate the error then being able to communicate the reasons for the classification of the error to yourself may be of some use, but that is not equivalent to successfully communicating the reasoning to the person who has committed the error.

On the other hand, if your primary goal is to signal status, then inconspicuously failing to communicate your reasons is good, as long as others do not point out your own errors. Which makes self-checking closer to sufficient.

Admittedly, that doesn't mean that this post's obligatory explianation is the best way to communicate reasoning either. Reliably successful communication is a hard problem, which means applying serious rationality to it.