The product manager as maestro - Orchestras are like groups of engineers.

I've formally been a product manager for just over a year and had the duties of product manager for at least three.  What I have learned is that the product manager job most resembles being the conductor of an orchestra. 

Like a conductor,  you choose the work the orchestra is going to play - the product that will be built.
Like a conductor,  you choose the feel and vision of the piece or product. 
Like a conductor you have to deal with players themselves - some virtuoso soloists or workmen like 3rd oboes - the engineers and operations folks. Like a conductor you have to deal with all the personalities and needs of the players - engineers have a way about them just like musicians.
Like a conductor you have to understand the business of the hall and that you may be beholden to the donors-  product managers are beholden to business stakeholders just the same way.  Make money and play the songs I want to hear the way I want to hear them.
Like a conductor timing is everything - having work sequenced and flowing is paramount.

Lastly,  conductors and product managers don't actually do the playing of the piece or the development of the work.  We work to help everything run smoothly to get the horns to play when they are supposed to or bring in designs when our developers need them. 
We're both looking for unity and flow within a larger group. Our job is to build trust so our players can play without the fear of making a mistake.  A good product manager like a conductor makes the individual pieces move as one - we make the sum greater than the individual parts.

Sometimes it can come out like beautiful music or a dissonant mess!