Why is it that Civilian Soldiers/Military believe their rank in service is relevant to what position they hold in civilian jobs?

it's not

There’s differences in management skills between a Team leader, Squad Leader, Platoon Sergeant, 1SG and CSM.

Because they are power hungry. I worked in a Military Unit as a civilian, there was another civil servant who worked in the Department who was a Navy reserve Captain, he believed that he had the power of a Navy Captain even though he was only a GS-11. I changed my cubical name tag to read Capt. Allen Parker and in very small print I put ( USAF, Ret )I was a GS-13 at the time.

That's because many, if not most, of them got that civilian job as a direct result of the rank, experience and training they acquired in the military. I know for a fact that is true in my case. I'm a govt contractor and in many cases I get chosen to be the one to go meet with the program manager (an army LTC) base solely on the fact that I am a MAJ in the Army reserves.

Usually NOT relevant to civilian jobs, but some feel it is something they earned and mistakenly asume civilians must comply.

Good question. Depends on the who is doing the hiring. I have advised numerous former military (and hired as many) on how to write a civilian resume. A former military person may understand the relevance of the grade to the job being applied for. However, as fewer people have military experience using rank as a sole experience indicator in not very relevant to many civilian firms. It is much better to described the job. Such as, As a Plt Sgt I was the second line manager to 30 individuals with responsibility of...., a payroll of, manged x lines of x no. of tracked vehicles valued at X dollars. In other words tell the story of what the job was and tie it into resource management, equipment management, skill sets used and managed, accomplishments - especially if it can be tied in revenue, cost avoidance and or improvements in performance, etc. And always follow-up after an interview with a written note of appreciation and use it to embellish on a point you may have felt wasn't too well addressed during the interview. In any case do not be too wordy.

Well the bottom line is it is not always what you read or hear that is the truth. I have been out over 20 years now and have retired from my civilian job and was glad to do so. The Civilians have this all figured out. I had several Jobs in civilian life Twice I heard conversations that I wasn't trying to over hear but just happened that way and they came out basically that Civilians will pretend they don't have an idea of what your worth is so they can Hire that kind of experience Cheap. It is about the Money. My last boss was former air force read all my paperwork still offered me the job at $1.00 less than my civilian counterparts. He told his assistant Production manager (this I over heard) always Offer Soldiers less they need the job so they will take less and work like two employs. Tons of things I could tell but you all get the Idea. JMTC

There are ranks in civilian jobs? I musta not gotten that memo.

In my experience, its how relevant one makes their overall skill sets to the job to their employer.The ladder will always be climbed from the ground up.
My current position in the civilian world actually holds more relevance to my MOS more so than my rank.

It is a shock when you come to the realization you have start out at the bottom again.