I have the same problem with certain lines. It's not the reel. It's not the fly (a problem with the fly construction - especially with commercially purchased dry flies - is the cause for leader and tippet twist).
The problem is casting and line taper (weight distribution beyond the tip).
To explain the casting problem, to save space, I need to use an analogy - pitching a baseball.
But, to get ahead of myself - it really means you need to develop an awareness of the path of the rod during the forward (mostly) stroke.
A line cast perfectly in verticle plane is rare. A baseball thrown forward in a perfectly verticle plane is rare.
Use the elbow as reference for the pivot point for the plane of energy going forward.
If you've never pitched baseball, watch them. Some pitchers' hand and ball travel forward on the outside of the elbow, and come across their chest toward the left leg.
Other pitchers bring the ball forward inside the elbow and go either straight or slightly out and away from their main body.
Casting a flyrod is similar, as far as the forward motion in relationship to the elbow, and the natural direction of the individual's forward motion of hand and forearm.
Everyone is a little different.
My build and natural tendency is to come across from outside my elbow toward my left. It always gave me the best leverage for slinging baseball.
The flycasting motion of energy is similar, though the casting stroke is not.
Casting at an angle to the verticle plane will impart twist into the line. If the amount of line (and its diameter) in the air is greater than what is still waiting to be carried forward, twist will occur.
It really gets to be a problem with weight forward lines if the head of the line is in the air and you have running line at the tip of the rod. It will happen on double tapers if you have beyond the mid-line transition in the air before you shoot forward.
I've experienced the problem a lot with Triangle Tapers.
The solution is to be aware of your verticle plane, the forward direction, and to not have as much line in the air before the shoot forward.
As far as changing the nature of your body to propel objects forward, there's not much you can do, except what works for you as an individual.
Hope that makes sense.