Why didn't Robb head straight for Riverrun down the west side of the Trident from Moat Cailin, circling around Greywater Watch? Instead, he stayed on the King's Road and had to bargain with Walder Frey to cross at the twins.
2 Answers
The King's Road is the only safe passageway through The Neck, which extends from about Moat Cailin to some point past Greywater Watch. The Neck is very treacherous terrain, filled with swamps and quicksand. It's mentioned that only the crannogmen are able to traverse it safely.
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Also Robb Stark would have wasted precious time marching around Greywater Watch, allowing Tywin Lannister time to react to Robb's march towards Casterly Rock.– RobertFCommented Apr 20, 2014 at 4:05
I think Sconibulus covered the main point - the Neck is treacherous land which is safely traversable only by those who know it well. I would also add that even if Robb and his men knew how/where to go to cross the Neck away from the King's Road, that this would still be impractical to actually do given the large number of men/horses involved. It's unlikely a safe passage could be found for such a large group travelling together, and if it could, there would likely already have been a road built on it sometime in the past.