Not only is the press perfectly safe for the shoulders -- as evidenced by the fact that shoulder injuries are the least-common injuries for Olympic weightlifters who use the barbell overhead -- but the correctly performed press is the best exercise for keeping shoulders strong.
The body is amazingly tough at handling abuse. But do something a hundred times, do it regularly, do it when you are tired, when your shoulders are already sore... something is going to give. Something. Is going. To give.
One of the things that amazes me most is how neglected this vital region of our body is exercised and understood. When I go to the gym rarely do I see someone training the all-important rotator cuff (RTC) group or its synergists -- the scapular rotator/stabilizer group.