The elbow of an expert thrower does two things during a forehand throw.
1. The elbow moves forward.
2. The elbow straightens.
And it happens in that order. Poor throwers generally struggle because they are leaving one of these steps out.
Why does the elbow have to do these two things?
Firstly, the elbow moves forward to give momentum to the arm, by rotation at the shoulder joint. So the elbow has to start behind the body. This is easier if the disc is upside down.
Once the elbow has moved as far forward as it can, the hand needs to move forward. This is done by straightening the elbow.
The last steps are wrist snap and finger snap.
The momentum is transferred to the disc late in the motion. It is at the end of the chain.
Another way of thinking of the motion is: shoulder, then elbow, then wrist, then finger. The snap of a good forehand involves the whole arm chain, with all joints used in a particular order.
Matt Dowle is a good example to watch.