The forearm moving laterally across the body (after pitch release) is a result of forearm flyout. It isn't forearm flyout. Forearm flyout is the extension of the elbow in addition to the internal rotation of the humerus into release as DM stated.
Every traditional pitcher has some form of forearm flyout, but it can more easily be "seen" in pitchers with a low arm slot such as sidearmers. Some pitchers finish with high, slapping themselves on the glove arm bicep/deltoid area. Some finish lower near the hip.
Forearm flyout MAY be a problem if there is too much reverse rotation, not enough shoulder rotation before release, or throwing too much around the front shoulder. You basically want to control this flyout into release.
A few ways Marshall tries to eliminate forearm flyout is ridding of external rotation, raising the arm slot, no reverse/counter rotation, over-rotation of shoulders into release, etc.
Pushing the ball has to do with poor "connection" between the arm and the torso and can be caused by a number of things including exhibiting little external rotation, no scap load, premature scap un-load, or premature humeral adduction.