Every time I see a video of someone doing push-ups, there's always someone in the comments saying about how the form is bad. I was always told my form was bad, but was never told what to do to improve it. Are push-ups just some Emperor's New Clothes kind of thing where nobody knows how to do one, but everyone needs to pretend to know so they don't seem like un-fit idiots?
Does it exert your triceps? Then it's a push-up.
If anyone tells you you're doing a push-up wrong, your response should be "fine, I'll just do something else". If they say 'you could more effectively target certain muscle groups' then that's worth considering iff you want.
A learning curve to fitness just serves to make it inaccessible to people, and to make people snobbish about it.