"Only an idiot can choose to believe something. To select your beliefs on the basis of what you'd like to be true like some sort of pick 'n' mix is ridiculous. For a belief to be rational, there must be some persuasive reason to support it. Faith, by definition, lacks that vital evidence which is why I cannot 'choose' to have it."

The problem with this reply sir is that you assume the meaning of the word 'belief' to be completely transparent , when it most certainly is not. For the sake of explanation consider the word 'true'. Here are three assertions that utilise the word 'true':
1) The claim 2 + 2 = 4 is true
2) It is true to say that there are 2 cups on my table
3) Peter Hitchens is a true Englishman
The word true has a slighly different meaning in each statement. The first concerns semantics and is a necessary truth. The second is a contigent truth concerning circamstances. The third is an appraisal and does not easily fall under either of the previous two categories.
Similarly, the words rational and belief can be plausibly used in more than one way. Consider the following statements:
1) It is rational to believe proposition x, if and only if x is self evident or follows as a matter of deductive logic from already known propositions (self-evident or deduced from self-evident).
Philosophers have been debating 1) for centuries without apparent resolution.
2) It is rational to believe empirical claim x provided there is much evidence supporting it.
Anyone that endorses Karl Popper's philosophy of science must reject 2), although common sense would seem inclined to defend it.
3) It is rational to believe that x is true provided it explains a state of affairs no worse than competing explanations and for which there are practical reasons for its endorsement which competing explanations lack.
I interpret our host as endorsing 3) for religious belief. If I am correct, then the notion of choosing a rational belief is not ridiculous in context. One might disagree with the reasons that our host gives, but they are not obviously absurd.