There's two huge aspects of management that gets diluted when it's compared to "managing" an LLM: - labor laws. You need to know those in the country where the employee has their contract, because this will restrict what you can (and must) do in your managerial role - Empathy. Managing humans is extremely messy and requires a ton of EQ to do well (parents have first-hand experience of this).
So, i.e: comparing being a manager to real humans vs instructing a next-token generator dilutes the skill of being a good manager and leader.