Actually, in the
Underground thread, I came to wonder the same thing.
First of all, it was the longest road. And by the time they set out, the Gap of Rohan was still within the spectrum of possibilities.
What spoke against the High Pass was mainly also what spoke against the route from the Carrock southward, namely what lay on or near the way: the Gladden Fields, that were probably still in the grasp of Isengard or Mordor, which searched there all the time just recently; wide open and clearly visible lands to the East held by Mordor; and, not least, Dol Guldur, to which the Fellowship did wisely not to expose itself too long.