I'm sure you will get a lot of good opinions, but here's what I suspect is happening without actually seeing you cast.
When a the line is still curved around a "U" shape (the loop) and you pull quickly with the rod the line actually accelerates around the loop. The harder you accelerate the rod at the start of the cast, the more the leader and fly whiplashes over the curve. So much so that it becomes like a bullwhip and snaps off the fly.
Think of the bullwhip for a minute. The way to make it go >snap< is to generate excessive force going one way (in this case forward) then pull it in the opposite direction well ahead of it's natural cadence so the tip whips around itself so fast it actually breaks the sound barrier.
Now think of this - let the bullwhip lay out completely and fall to the ground. Then pull it as hard as you can and it will never make the noise even if you pull it twice as hard.
Next let the bullwhip lay out straight but not fall to the ground. Then pull it back to lay out in the other direction. Now that's a fly cast.
The concept of a fly cast is to lengthen the line in the air completely without letting it fall to the ground, then at the moment it's suspended yet still taught we pull against that to load the rod in a forward direction.
It's important to start the casting stroke with a "clothesline" tight line but don't hit it hard at the start. Maintain the feeling of tightness but ease it into the reversal of direction, then accelerate to a sudden stop once the momentum has turned.
Most likely you are not allowing that transition to complete before applying rod force.
So to summarize:
1) allow the back cast to just about lay out straight like a clothesline suspended in mid-air for a split second. If it does not lay out flat then you need to practice getting that rod loaded on the way back before you stop. Use only as much force as you need.
2) Ease the line through the reversal of direction. Don't accelerate till the momentum has turned.
3) Make sure you feel like you are stretching the line with the stroke, not snapping it. In fact you are stretching it, like taffy.
Let us know how you fare.
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