You can have a certain number of explanations why
North Kingstown (R.I.) is the Skippers. Go with the most obvious answer, though.

Photo courtesy of Wikipedia
Pretty much anybody could agree that the school might be talking about how its athletes and students get around. Maybe they don't bother with walking and running - maybe they just skip from place to place.
Another possibility could be that this school has a connection with Barbie, and wanted to give her underappreciated sister Skipper some publicity. Unlikely, but possible.
Or maybe we just take the simple route and say that it has to do something with a ship captain. That one makes much more sense.
North Kingstown is located on the western shores of Greenwich Bay and the city has a history tied to maritime activities. And a whole bunch of history in general, as the town was founded some time around 1674.
They had the choice to be Captains, Navigators or Sailors. They went with Skippers, and in a state that only has two mascot names not seen anywhere else in the nation, it was a pretty unique choice.