Pure speculation here:

Hard-shell cases were not nearly as common in the early days, and a gig-bag was usually not something specifically made for a guitar. So holding the neck near the headstock and slinging the guitar over your shoulder was an easy way to carry it. Much like an axe.

Related thought:

If you wanted privacy to practice, you had to go out to the woodshed, to work with your 'axe'.

... or something like that?