Tug/tugboat are new words for me. I checked them and I think "tug" here simply means "pull/tow". I think if the barges are at behind, the movement should be called "pull/tow". So why "push"?
I think I know why now. In my mind all tugboats should work like this. (Links of pictures just for illustration.)The sentence is puzzled by the same thing. Tug means 'pull', but tugboats push barges, and push is the opposite of pull. The joke is to point out that it is strange that we call them tugboats, when what they really do is push. Maybe they should be called pushboats.