BILL— Here’s the scoop on pirouettes. Most of the time if you’re having problems with them, it has to do with the quality of the canter. Is it collected enough? Is it balanced enough? Can your horse keep enough jump behind, maintaining the tempo while not being held back by the reins as you make his strides shorter? These are things that you must practice over and over, building his strength and confidence before you try to put him too much on the spot or do too many strides in a row.

Then you have to make him easy to turn so he wants to follow your weight. If he doesn’t, you’ll be inclined to use too much outside leg, chasing him around and making him lose his lateral balance! Remember, you should still be riding him “inside leg to outside rein” even as you are turning his forehand in the direction of the bend.
Pirouettes ridden without the rider’s inner leg support often devolve into something like a spin. When I see one I flashback to that scene in the diner in Five Easy Pieces.
[Provided here for the too-young or the old-and–forgetful:

https://www.youtube.com/watch?v=6wtfNE4z6a8   When Jack Nicholson sweeps everything off the table in disgust at the waitress giving him grief, think “Very bad pirouette!” It comes right after the iconic “You want me to hold the chicken?” exchange which is always worth another viewing!]

Alternatively,

the image Major Lindgren drilled into my head is of cutting slices of an angel food cake – down, up, over, and down again. No hurry at all because the horse stays in lateral balance between the rider’s legs.
There are many exercises you can use to create these qualities that make good pirouettes likely to happen. We’ll look at those next time.