A recent poll of a large number of households found that 47 percent of those with a cat had at least one person with a university degree, while 38 percent of households with a dog had at least one person with a university degree. Clearly, people who hold university degrees are more likely to live in a household with a cat than one with a dog.
The statement 'ignores the possibility that a significant number of households might have both a cat and a dog' is the reasoning in the argument that is flawed.