I've seen questions and arguments about how the airline pilot uniform came about and and whether it, and the profession, is based on the military. I've been bored so I did some research-

The historical predecssor to the aircraft is the ship. Since Viking times the person who controlled and navigated the ship was called a batsuen (Anglo-Saxon) or boatswain, which literally means ship's husband. Later this position was also know as the ship's master. Also since that time period the fighting men on ships fitted for war were commanded by the nobility. The nobility had officer commissions from kings as captains, lieutenants, etc., but they were untrained in navigation and ship handling. The men who actually did the navigation and ship handling were essentially civilians who were given a "warrant" (warant is an Old French word meaning an authorization). A warrant is a commission, or legal authorization, that is given usually by a body such as a governmental department or court instead of by a king or president.

Skip ahead a thousand years to the 20th century- During WW1 our harbours were mined by a combination of civilian and Army mine planting ships (the Coast Artillery Corps). in 1918 it was decided to place all this work under the military. The commanders and first mates of these ships were given army commissions as warrant officers. The ship's master had a rank of 4 stripes and the first officer had a rank of 3 stripes. This continued through the 1920s and 1930s at the same time as airlines and airline pilot uniforms started. That's where the idea came from.

So, although airline pilots are not part of the military they are part of that same tradition. And like hundreds of years ago they fulfill a military transportation role. They also operate under a warrant, or authorization, just like the boatswains of old.