It's true, pushups do screw up shoulders. Been there done that.
Agreed.
And I've been doing them wrong for like 2 years. But it's imo most complex exercise to master.
Nah, to both of these.
Both push-ups and bench press mess with shoulders when done improperly, without good opposition work, and without adequate shoulder training and mobility work. But done properly, push-ups aren't harmful at all for the shoulders. Just because a few people's anecdotal stories about push-ups messed up their shoulders, this doesn't mean the exercise is harmful. I guarantee I can find a far larger number of people who have had their shoulders fucked up by bench press. The problem is people tend to do both exercises with poor form and inadequate work for both shoulder strength and mobility, and opposition muscle groups.
To the second point, bench press is complex as far as standard bodybuilder exercises go... but nowhere near the three O-lifts... Clean, Jerk, Snatch. The technical aspect of those three lifts is in an entirely different realm from any of the power-lifts.
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You don't really have to do anything. If you want to be a powerlifter then yes, you have to bench press. If you want massive pecs, yes, you have to bench press.
If you want to be fit and have a bit of muscle, you can sprint and do pull ups and push ups. It'll never get you as beefed up as you can be, but it depends on your goals.
All one has to do is look at gymnasts to realize that there are many ways to add muscle mass to a frame including bodyweight exercises. Disadvantaged leverage positions, such as those required in gymnastics build muscle very quickly.
I don't bench at all anymore. Not because of shoulder problems, or anything else like that, just because I don't see the point of the exercise if I'm not a powerlifter or a professional (american) football player. Yes, if I wanted to have a roided up bodybuilder style physique, I would bench press. But I don't want that at all.
I do planche push-ups, handstand work, and gymnastic ring work (muscle-up, iron cross, inverted iron cross, maltese cross) for my chest and shoulders. Add to this regular shoulder mobility work. The last time I benched, after 16 months away from the exercise, I was able to do 5 sets of 3 @120kg (bodyweight 75kg) without a spotter.
There are many ways to develop a strong chest, shoulders, and triceps aside from weightlifting exercises.