While it's true that some wonderful voice teachers are not active performers for a variety of reasons, the old adage, "those who can't, teach", is often a misrepresentation of what is really the case when it comes to performing and teaching.
In my own circumstance, I've become a better singer because of my teaching and a better teacher because of my personal performance experiences, passing what I've learned on to my students. I hope that I practice what I preach when my students see and hear me perform. I also want my students to find their own authenticity when they sing and not just be a carbon copy of someone else.
On the flip side of this subject, some of the most gifted singers do not necessarily make the greatest voice teachers. They often do not have the time, patience, empathy or passion to embrace the learning process in a younger, less experienced singer.
There sometimes seems to be a stigma about singers who teach. This doesn't appear to be the case in the instrumental field. Maybe there is a prevailing assumption that teaching wears on the voice, or that one cannot travel and be away for extended periods of time if tied to a academic teaching position.
Here's what I know to be true from experience:
I've learned to let my students sing more during their lessons and for me to demonstrate/model less. I must also support my speaking voice when I teach and methodically warm up my singing voice prior to conducting my first voice lesson of the day. Rescheduling lessons on the day of a performance is optimal and yields my best results, physically and mentally.
Lastly, professional singers who also teach shouldn't buy into or perpetuate this skewed sense of an either/or stigma, We can achieve balance.
I'm reminded of something Kristin Chenoweth said last summer at the Hollywood bowl after local voice teacher, Sarah Horn, sang an impromptu duet with her from Wicked; "This woman is teaching our children!" Imagine that, someone who can really sing can also teach!