There's also nothing stopping a good dev from being a great manager, or vice versa. A good dev learns to listen well, which is also a key skill as a manager. A dev creates working systems out of conceptual components, a manager creates working teams out of actual people. The biggest difference is that there's no Stack Overflow for management - every situation has to be treated as unique and you can't just copy-paste the solution.
This is in my opinion actually quite easy to explain to managers: asking for time estimates in software development is like asking for time estimates in proving a deep conjecture in mathematics.
Since every economics major has to take some courses in mathematics (which at least in Germany are often there to weed out bad students), this should not be difficult to understand for managers.
The problem rather is that these clueless non-technical managers insist that this perspective is simply wrong and theirs is right.
"Why can't you hit a hole in one with every golf shot? You know exactly where the hole is, you know how much the ball weighs, you know the length of the club, you know how hard you need to hit it and in what direction. So why isn't every golf shot a hole in one? Because, obviously, you may have miscalculated how hard and at what angle you should hit the ball, you may not have the skill to hit the ball exactly right, and any amount of random factors can affect the ball between you hitting it and it arriving at the green. Same for software development"
This is exactly my point: at least in Germany, the compulsory "mathematics for economists" courses are there to weed out student and are thus feared among the respective students.