Ted Williams was quoted as saying that "hitting and pitching are the same" when it comes to teaching and coaching those skills. Who am I to argue with the most gifted hitter in baseball history?! I will however try to explain that statement. Let's start with the hitter's back foot pivot. Every professional hitter digs in with their back foot before getting in their stance to enable them to get the most leverage against the ground to get the quickest and under-control pivot.
The pivot first activates the back hip, and then the back shoulder is released to the ball. When done correctly the hitter maximizes bat speed, which gives the hitter the most power out of his swing.
Power starts from the ground and goes up. That is why players constantly work on strengthening their lower body and core.
Pitching is taught the same way as hitting at the professional level and should be done at all amateur levels, but of course it isn't. The back foot should pivot off the pitching rubber to activate pitcher's back hip and shoulder to maximize their velocity and movement.
The pitcher's weight should be on the inside of the back foot to make the pivot easier, and the foot should roll and lift after the pivot, which makes the hip and shoulder fully rotate behind the ball in an explosive and dynamic manner.
If the foot drags, the pivot is not being executed and the back side becomes misused and lifeless. Most likely the pitcher is pushing off the rubber. Pitchers should never push-off.
On MLB network the pitchers and their staff were talking on about this topic. They all agreed that not one major league coach teaches the push-off technique, and if they did they would be fired.
Why is the push-off wrong? Because it pushes a pitcher's upper body ahead of his throwing arm causing a late release of the ball to the target and the inability to command and locate pitches.
Secondly, push-offs do not activate the pitcher's back hip and shoulder to the fullest extent, which robs him of power and velocity.
Lastly, the technique puts undue strain on throwing arms, which greatly increases the chance of injury.
Do hitters ever push-off after digging in? No, and pitchers should never pushoff either. I have heard too many youth coaches teach pushing-off, and it is a recipe for disaster, physically and fundamentally.
Remember this youth coaches who want to teach skills correctly. Pitching and hitting are the same.