The upper arm mobility to be able to perform the bench press correctly relies on the position of the scapula (scaps) and the position of the rib cage. If you have not read the thoracic mobility go back and read that one to understand the asymmetrical tendencies of the rib cage and scapula. Looking at the bench press, the movement starts with the arms in a reach position and the person lowers the bar down to the chest tapping the upper pecs, reversing the direction and pressing the weight back to reach position, extending the arms.
Limitations in shoulder extension, arm internal rotation and horizontal abduction can lead to poor shoulder mobility. These limitations can lead to compensatory actions by other muscles, the anterior neck muscles will kick in to help and creates tension and tone through the muscles from the head and neck to the upper ribs. Another pattern that is seen in shoulder pain, a most common issue, is anterior glide of the head of the humerus when the elbows retract back past the rib cage. This can stem from poorly positioned scaps or not moving through the scaps to perform the bench press. This is a sure way to end up with cranky shoulders when working out and could lead to further issues with over toned muscles and potentially nerves.
To increase this we need to get the thorax to neutral and the position of the scapula correctly on the cage. Repositioning exercises like the 90-90 Hip Lift is a perfect one to get the sense of the rib cage in an exhaled position while maintaining this through breathing. We want to restore the position of the axial and appendicular skeleton before we start moving arms and legs with external load in it.