The push-up is underrated in the strength and conditioning world. Why? Because too many people do it wrong. They often set up with their hand position high and wide. If you took a snapshot from above, their set-up would look like the letter T. People do this to make the exercise easier. Why is this position easier?
I think there are a bunch of different ways you can do push-ups, none of them being “right” (although some are definitely wrong). Which ones you do is more a matter of what muscle groups you want to work than any one specific form being the “right” one.