It’s important to perform both Push exercises (push-ups, strict and push press, bench press, thrusters, etc) as well as Pull exercises (pull-ups, bent over row, high pulls, reverse db fly, etc).
When you do a lot more of one type of exercise than the other, the body gets disproportionate and muscle imbalances develop. This is why you may see big, hulky guys at the gym with extremely rounded shoulders and no shoulder mobility. They probably do a lot of bench press and other Push exercises, but not nearly enough Pull. People often neglect the Pull exercises.
Pull exercises are great for helping your posture as well. Pull exercises tend to work the back muscles, while Push tends to work the chest and the front of the body. Not exclusively, but in general. Pull exercises are an important part of functional fitness as they assist in everyday tasks you might be doing. Pulling a child out of a crib or bed for example is a Pull motion. I’d estimate that 85% of people that come to me tell me that they have a “back issue”. This is usually the lower back. While all “issues” are not the same, typically they take it so easy on their backs that they become incredibly weak and they become even more prone to injury in the future. It’s important to progressively and slowly start doing back exercises, ESPECIALLY if you have back issues. The back is what supports your entire body and without it life would be tough. Don’t neglect it!