Sample size of one, but in my younger and less careful days I have managed to injure my shoulders overdoing both push-ups and dumbbell bench press. I managed to injure my shoulders much faster doing push-ups, likely because there was no way for me to ramp up the weights slowly, since push-ups are always minimum body weight. With bench press, I injured myself when I got impatient and ramped up the weights too fast. With push-ups, I injured myself when I got greedy and did too many sets throughout the day, since it's easy to do and do twenty whenever there's a few minutes of free time.