Synonyms of 'fall down'
▷ See fall
That is where his argument falls down.
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If things or people disappoint you, they are not as good as you had hoped, or do not do what you hoped they would do.
He said that he was surprised and disappointed by the decision.
If someone fails you, they do not do what you had expected or trusted them to do.
We waited twenty-one years; don't fail us now.
Thesaurus for fall down from the Collins English Thesaurus
If an argument, organization, or person falls down on a particular point, they are weak or unsatisfactory on that point.