1. something that does not prove to be true, something difficult to believe
that argument/belief/excuse won't/doesn't hold any water (with me)
When you say something 'doesn't hold water' you mean that it is illogical or that the argument is not strong or that it is untrue. An argument or opinion which is considered to be strong or difficult to disprove is called a 'watertight' argument. An argument which can be disproven easily is said 'to have holes in it', and something which has holes in it 'can't hold any water'. You can use this idiomatic expression in both social and professional contexts.