Was going to edit my post but you beat me to it by replying.
This is the situation, in the book, Rob sent a diversion to Tywin's Army, whilst going to relieve Riverun from a Seige. If he succeeded, he would have gained the support of the Riverlords (So more armies). Delaying time would mean the seige has progressed further, so it is a count down there. Plus, Robb doesn't have the forces to defeat two armies. Each Lannister army is composed of 30,000 men each, Robb only has 18,000 at his command, and he just sent 2000 of those as a diversion, so he is currently facing Jamie's 30,000 with 16,000. What he has is the elemental of surprised and the fact they are seiging. He needs to act quickly and put the situation to his advantage.
He ultimately did the best course of action and the results in the book reflected that. What stood between that is the Twins.
Orange Line:
Fastest Route to Riverrun
Requires the Twin's
Element of Surprise
Pink Route:
Slower Longer Route
Facing 60,000 men with 18,000
No Element of Surprise
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