I think you’re trying to make a good points, but with the wrong analogies.
You’re right in saying that most engineers (coders) are overrated. Probably coz it’s extremely easy to be an average coder. You just need to be smart enough to know a language, read code and google well. We can build great things but ask us to explain why we did what we did and most of us will just mumble for a few minutes before saying that a blog post/stack overflow/OAI asked us to do it.
Product managers, on the other hand has more responsibility by definition, is a cross department stake holders and overall just has higher stakes. Some of the best engineers I’ve worked with transitioned to product roles.
To your original question on why people shit on PMs
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Title is abused. People who manage just excel sheets and WAs groups are also called product managers.
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It sounds easy. Everyone feels they could be a PM. It’s like SQL. Syntax is easy so you’ll always get answers but it requires a lot of skill to know if the answer is correct and what you did was optimised.
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Shit ton of companies that shouldn’t exist have existed. All of them are solving problems no one cares about and product people have romanticised the whole thing with jargon like cohorts, AB, DAU, MAU, Retention. The list goes on. Obviously, these are all important things but they are used more for making it sound important than actually solving in most companies.