Why would a flight from North America to Asia sometimes fly over the Atlantic?
Those routes are extremely similar.

They're basically two almost-a-straight-line routes over the arctic ocean, except that the second one has deviated a bit to the right, so that it's gone just on the right of the North Pole instead of passing by the left. At the pole itself, there's no such thing as "East" or "West", and if you pass very close to it, there is a discontinuous jump between passing it "going East" and "going West".

You can see this explicitly by going to FlightAware, asking to View track log, and downloading the flight tracking data to be viewed on Google Earth:




 Actual tracking data in white. Interpolations for the missing-data parts in green. 

As you can see, there is indeed a nontrivial deviation of what's probably several hundred kilometers in clipping Nunavut vs the northeast corner of Greenland, but that deviation is within the normal ranges of what you'd get in your standard transatlantic flight, say. The only change here is that the variation now includes the North Pole itself.