Line twist is quite common if you cast one handed with the the Belgian cast, which is an elliptical casting method for casting into the wind and for eliminating tailing loop knots. Some casters use this cast because it eliminates "wind" knots, eg, tailing loop knots and the cast makes it less likely that a heavy fly will hit the rod..
An elliptical stroke is when the back cast and forward cast occur in two different planes. Because the two strokes are separated by different casting planes, even if the lines cross in the vertical plane, they cannot form "wind knots" because they are separated in the horizontal plane.
For example if you do a backcast with the rod tilted to the side horizontally, and then bring the forward cast overhead, that is an elliptical stroke. The stroke is an ellipse rather than being 180 degrees from each other along a straight line as we teach beginners. Even if there is a concave rod tip path on the forward stroke that would normally allow the fly leg of the casting loop to tangle on the rod leg, they cannot because they are separated horizontally in space. Said another way, even if the loops cross vertically, they will not tangle because they are separated horizontally in space.
It can be used to cast heavy flies because it is a constant tension
cast. With the line under constant tension, there is not that stop and recoil from a heavy fly as it bounces back against the stop between a 180 degree forward and backward motion. That is why it is a good cast for heavy streamers and nymphing rigs.
However, by casting in an ellipse, we are moving the rod tip in a circle for each casting cycle of a backward and forward cast. For a right hander
this causes the fly line to twist counter clockwise
for each cycle. Take a look at how your fly line is twisted and I bet that you will find a counter clockwise twist for a right-hander and a clockwise twist for a left-hander.
To prove this to yourself, take a pencil in your like a rod and bring it back low to your side and then around the ellipse and forward high, then back low and forward high, over and over. Look at the circle your hand and arm are making and you will see that you are moving in a counter clockwise circle.
This type of elliptical cast is often used when casting in the wind, and is called the Belgian "wind" cast.
It is also used when nymphing when you pick up the line low to your side and then use a water tension cast to bring the cast back over your head. Then you follow the drift back and lower the rod to the side and loop over your head again. You are repeatedly casting elliptically.
To remove the twist, make a long cast downstream, and then opposite
clockwise loops with your fly line to remove the twists and then reel up the line onto the reel before leaving the stream.
Here's a video of the elliptical cast. You can see how he would introduce a twist with his casting motion.
"The disadvantage of this cast is that it throws a half twist in the line every cast. Half twists add up! So it's best to use this cast sparingly, otherwise you will have to get into the habit of removing the reel from the rod, every 30 casts, or so, in order to spin the twists out."
The Belgian Cast
The Belgian Cast | MidCurrent