The project manager is the surgeon of an organization

The PM's in the middle.  The person at the middle of all things (related to their specific initiative(s)) in an organization is the project manager.  Whether it's engineering work, communications, planning, or whatever, the PM is in the middle of it all (related to their objectives).  There are other stakeholders in the project team or organization that have more sway or power than the PM but the good PM always drives, and hopefully does so gracefully and in a relationship- and team-building way given this context of initiative and performance.  The PM knows how to operate on the body that is the organization supporting their initiative.  In this way they are both graceful, powerful, and dangerous; like a surgeon is.

Surgery and PM operations defined.  Google defines surgery as, "The branch of medicine concerned with treatment of injuries or disorders of the body by incision or manipulation, esp. with instruments."  To me, this is metaphorically similar to the actions of a PM (in my words), "The branch of business concerned with the identification and resolution of problems of an organization by direct involvement, action, esp. with tools and frameworks."

Similarities abound.  We can see the many similarities between the surgeon and the PM in that the PM is an operator and a skilled technician, operating on something (the organization and team and instruments to produce a desired outcome).

A balanced and skilled operator.  The PM is not held up on roles or titles, they have a specific mission to deliver a specific result, product, or service, and they are going to do it, by hook or by crook (but gracefully through the team).  The PM's goal is to figure out what work needs to be done from the various stakeholders.  The PM must know when to push and when to pull, when to cut and when to sew.  They lead very stealthily but when they push they push really hard and it's obvious; they can make a very deep impact.  Many people may resist the role of the PM but it is an important one:  The organization would not change as rapidly as is required for it to deliver the desired outcome if it weren't for the PM operator.

Not a tracker.  I'm not referring here to a PM who is a "task tracker" or anything of that nature.  I'm referring to a driving, smart, analytical, senior PM who is all about getting the best results possible on time given his resources and communicating effectively at all levels in between.

Concluding thoughts.  As you can see, there are many similarities to a PM operating on an organization to create a result and a real surgeon operating on a body.  They're deep in the weeds of the operation but can come up to a bird's eye view to understand the context and next courses of action.