When we first meet The Big Lebowski he tells The Dude that the bums have lost, that his revolution is over, and that he needs to go and get a job. While being rather heavy handed in his statements could he have legitimately wanted something better for The Dude?
In a way he was an older version of The Dude in that he helps strangers with their problems, is unemployed, and is only given a limited amount of funds to live on. Could it be that The Big Lebowski didn't want to see The Dude in a similar situation, used by nihilists?
I suppose I could be wrong though. After the situation presented itself he did decide to throw The Dude to the wolves and take what he thought was entitled to him.