I thought I would address this question because I have often been asked "can you ski black runs?" by people I am teaching. It is usually children that ask, but adults do as well. I find this staggering really, considering what job I am doing. It is a bit like asking a driving instructor if they have ever been on the motorway, or a maths teacher if they can multiply.
To teach skiing you need to be able to demonstrate techniques accurately, which means performing them consistently even in difficult conditions. You also need to be able to take customers onto more difficult terrain when they are ready, and you need to be seen to be skiing well at all times. For all these reasons as well as safety issues of travelling around the mountain, yes you do need to be a good skier to instruct. That does not mean being a world class competitor, although many world class competitiors have gone on to be great instructors and coaches. It does mean (as a minimum) being comfortable skiing any marked run in resort at high or low speed.
There are many criteria on which instructors are tested, and the level increases for the higher qualifications. Of course good skiing is relative, and many a top instructor would look quite average beside a world class racer. However, to qualify to instruct you do have to reach a level that most recreational skiers would call 'good'. Personally I prefer the word competent, as in competent to do the job, or competent to ski the whole mountain.
I was looking for a photo of me on a black run to illustrate this post (and prove the point), but all I could find was this warning sign from the top of a double black diamond run in New Zealand. I remember taking the photo because you never see signs like this in Europe. For one thing, anything approaching extreme is off piste and unpatrolled, and for another, extreme is another pretty subjective word. If something is skied often enough to warrant a sign, some would say it is not really extreme.