That might be true for you, but it's not true for me
Dawkins retorts, "You mean true for you is different from true for anybody else?"
In this response, Dawkins means that to say something is "true for you" is to deny the existence of facts independent of anyone's beliefs. If O'Reilly's statement is a true reflection of what he thinks, he must necessarily reject of the concept of objective realities (usually considered synonymous with the term "facts") and dismiss methodological empiricism (i.e. observational science).
Though O'Reilly's statement itself was likely made without consideration of its implications, the argument in general infers that the person considers his own reasoning and intuition more valid a foundation for belief than reason, and empirical evidence.
This argument can be interpreted as an assertion of relativism.