Are you trying to win a debate or help your friend to expand his thinking? If you're trying to win a debate, neither of you will win because you and your friend are not debating by the same set of rules.
"What are some good arguments for dismissing thoughts that contradict rationality?"
Thinking that contradicts rationality, by definition, tends to ignore rational arguments. Rational thinking tends to dismiss non-explicated assertions.
These systems of thought (theistic religion and atheism), do not work in the same way and are not compatible for the most part.
Sure, we can identify features that exist in both modes of thought: Emotions, Art & music. Or identify commonly-held beliefs: Morality, love & concern for family, friends and strangers. Still, the fundamental "operating systems" are simply not compatible: Rationalism requires evidence to accept the Resurrection (you said your friend was a Christian); simple assertions do not work. Religions have their own rules, usually including faith in some set of prescribed set of beliefs.
That said, If you want to help your friend to expand his thinking, read some Joseph Campbell yourself and TALK WITH (not necessarily ARGUE AGAINST) your friend about your interpretations. Campbell is probably a good choice of reading for your friend as Campbell expounded on "the sublime," -- impressing the mind with a sense of grandeur or power; inspiring awe, veneration, etc. (dictionary.com) -- but rejected religious ideology. This really sounds more like what your friend is talking about ... Except for the Christianity part ...