Some say you shouldn't press overhead because it's bad for your shoulders, but that's only true if you have a current injury.
If you notice that the front of your shoulder drops down and your elbow flares out, then your shoulder is about to go tits up and you're going to get some impingement. When you let your shoulder drop, your rotator cuff can become compressed under your acromion (which is a bony process of the shoulder blade).
When doing the standing press, keep the elbows up and tight to the body. Squeeze your shoulder blades together to keep your shoulder in a neutral alignment.
The next time you do a standing press, do a quick body positioning check.
- Stand with the feet shoulder-width apart.
- Lift the chest and elbows.
- Keep your head neutral.
- Engage the core as you slightly lean back to press the bar.
- Keep your elbows lifted as you begin your press.
- Pull the body through once the bar gets past the head.
- Shrug the shoulders up at the top of the press as you "stretch the bar."
Following these steps will increase your pressing ability and keep you from destroying your shoulders in the process.