Something I learnt when I was working in Silicon Valley is that managers are not "bosses" but rather folks who enjoy working with people and whose task is to make sure that everybody on their team is happy and productive.
Becoming a manager is, or should be, a career choice rather than a way to get a promotion or raise.
My Point of View
IMO the best thing that leadership can do is delegate and trust, help folks develop that sense of ownership and make sure that teammates can deliver in a way that is efficient for everybody – this can take some time and practice.
A manager should focus on helping folks become autonomus, grow and own a piece of the company. After all work is not kindegarden and workers don't need to be held by the hand or checked and "scrutinized" constantly: a good manager knows when to step back and let their team take care of things.
Once there is that, then the manager's responsibility is to sync up with individuals periodically and be available for brainstorming, provide advice, alleviate "pain" and solve folks' work-life related problems.
In the end management is for empathetic and caring people who put company and individuals' interests on the same level and want both to succeed.
Sometimes it might be necessary to be a bit tough but otherwise, to me, a good manager is the one who manages to keep stress out of the way.
Relationship between engineer and manager
@sangster wrote an amazing thread about enstablishing a good relationship with your manager. I highly recommend you to read it!
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