Argumentum ad Speculum

Hypothesis Contrary to Fact

This fallacy is similar the Faulty Analogy Fallacy. It occurs when credible support is not provided and, instead, hypothetical examples that are factually incorrect are used.

Example: 

If Mr. Spagnolo had been born as a three-legged Catahoula Leopard Dog in the slums of Johannesburg, his parents, who would have been blessed by not having to raise yet another child, could have become wealthy strip mall owners in Branson, Missouri.

Mr. Spagnolo, in fact, was not born as a three-legged Catahoula Leopard Dog in the slums of Johannesburg, making this argument pointless.