Usually teaching is a meta activity such that when I am teaching an activity like gun handling and safety, or Katori, working on my skills takes a very backseat to the main activity of helping the student work on theirs. This is in no way to imply that teaching is neither very enjoyable (which it is), nor that one can not learn a great deal about a subject by having to articulate that subject to a student (one can); but for most activities one cannot teach effectively and practice at the same time. Teaching and training are different skill sets, each with their own craft.
For instance, when I teach Katori at my dojo in Mordor (Maryland), there will be 18 -25 students on the mat and the act of concentrating on their technique means that I have little time to train on my own. Even if I pair off with one of the senior students to train in a two-person exercise, I am primarily evaluating their technique, and only secondarily my own.
And since Katori mandates that all new techniques are taught by those with a teaching license, I spend much of my time on the mat teaching a new kata (form) to students. When I am thus engaged, there is not much opportunity to work on my own technique.
But teaching taiji is a little different. Like Katori, when teaching taiji I spend most of my time working with new students, leading them slowly through however much of the form they have been shown. But although learning the form is important, and hence I have to lead people through the sequence (the external movements), learning the sequence is not the end, but rather the means to develop the internal integrations of shen, yi, qi, and jin. Thus, when leading the class slowly through the form, not only CAN I concentrate on taiji principles (internal in nature), I pretty much HAVE to in order to lead the class correctly.
Of course one has to spend some time doing the meta activity of simply observing, and correcting. But much of the class is spent simultaneously both teaching taiji, and practicing taiji. Hence, after teaching even a very basic class for an hour and fifteen minutes I am quite exhausted – not so much physically, but mentally.
To put all this a little differently: Although I love teaching Katori I cannot say after a two hour class at my dojo that I have practiced much Katori. Similarly, when I giving instruction on sight picture/sight alignment and trigger control, I am not myself getting any practice with the fine motor skills involved.
But when I am teaching taiji I pretty much of necessity have to be doing (at least internally) what I am teaching.
That is why even though I sometimes teach at a senior center, where most of my students are older, I can consider the time I spend teaching there not as a diversion from “good practice”, but rather as additional practice time.