Originally, 'hold water' related to containers keeping liquids without leaking. Metaphorically, ideas should not 'leak' flaws. A basket can't hold water, just like his excuse can't hold up under scrutiny.
Pro Tip 2/3
Critical Thinking
Use 'not hold water' when you critically evaluate something and find it lacking in substance or reason. His explanations for the errors in the report just don't hold water.
Pro Tip 3/3
Skeptical Tone
The phrase often implies skepticism or doubt about the validity of the argument or idea. The board found that the manager's justification for the overspend did not hold water.