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In Heinlein's defense--if his character did say this, and if it was said by one of those fatherly "voice of Heinlein" characters, which I'm quite prepared to believe...
I would've read the quote as saying, in effect, "If a seemingly logical argument proves something I regard as absurd, I will be skeptical." That was, after all, the appropriate reaction for the person confronted with the proof that 2 = 1. The first reaction ought to be, "Well, I know 2 doesn't equal 1, so no matter how nice and logical the proof seems, there must be something wrong with it." Maybe then you look at the proof a bit harder and see the div-by-zero error in step 5. But if you don't find the error, you don't then run off and rebalance your checkbook based on your new knowledge that 2=1; rather, you say to yourself "Got to be a problem in there somewhere", and wait for someone to show you where it is.
So I would assume, in the book, that some sensible character offered a perfectly sensible argument why the heroes should believe something implausible, or do something they felt deep down that they oughtn't. And Fatherly Character responds by saying, essentially, "Just because you have an argument that seems solid right now, isn't enough reason to do something you really feel is wrong--it's more likely that there's a flaw in your argument that we haven't spotted yet."