Final answer:
The irrelevant and insubstantial support is McKinley's reference to divine inspiration for keeping the Philippines, lacking concrete evidence.
Step-by-step explanation:
The sentence that is a clear example of irrelevant and insubstantial support for an argument is: "President William McKinley, explaining what he believed was divine inspiration on behalf of maintaining the Philippines under American rule to Methodist leaders in 1899."
This statement cites McKinley's divine inspiration as a justification for maintaining the Philippines under American control, but it does not provide concrete, evidence-based support for the argument and could be considered more of a personal or spiritual rationale than a substantive reason.