'A watermelon!" I shouted at the Archbishop of Canterbury. "She said that she carried a watermelon!"

Yes, it was a standard Wednesday night out for me: explaining the plot of Dirty Dancing to the leader of the Church of England.

I think Dr Williams has seen the film anyway. But it's hard to be sure. I didn't really let him get a word in.

Having been invited to a reception at Lambeth Palace (in error, I assumed, as I hurriedly accepted before the mistake could be rectified), I had been taken aback to see the archbishop actually standing in the doorway. The Archbishop of Canterbury. My jaw dropped. I clasped his hand. I gabbled something incomprehensible. I am a fan of his and I did the fan thing.

"Well done," muttered my friend Charlie as we finally moved through the doorway and into the reception. "If Lou Reed is standing in this room, I don't think I'll be able to embarrass myself as much as you just did."

Sympathetic, perhaps, to my star-struck awkwardness, the kindly Dr Williams came to talk to us again. It was an opportunity for me to be a little cooler. Say something witty, perhaps. Or wait for His Grace to speak. Or Charlie.

Instead, I apologised for my random opening remarks by way of a rambling soliloquy about the moment in Dirty Dancing when Jennifer Grey sees Patrick Swayze in a nightclub and fancies him so much that she can say nothing more sensible than: "I carried a watermelon."

Oh yes. In this scenario (I realised too late to stop talking), I was Jennifer Grey. And the Archbishop of Canterbury was Patrick Swayze. The grinding, bare-chested target of Jennifer's summer lust. I have racked my brains, in the nights since then, over whether I could have come up with a less appropriate analogy. After some reflection: no. On the plus side, I have worked out that my pillowcase might make a very effective noose.

My stammering admiration for the Primate is not, I would like to make clear – to the lovely Mrs Williams, if nobody else – a lustful one. Great beard, but no. It is because he is unashamedly, undeniably, publicly and unarguably, both a believer and an intellectual.

Joan Collins said that Cheryl Cole inspires slavish fandom because the people of the 21st century are starved of beauty in the public eye. That's how I feel about the combination of brains and faith. My list runs out at Frank Skinner and Ian Hislop. (My list of famous babes is much the same, but slightly longer.)

There must be others, but they keep it quiet. Lord Carey, a previous incumbent, complained last week that Britain is ashamed to celebrate Christmas as a religious festival. It's bigger than that: people are embarrassed to believe in God at all. They feel silly.

There is a new, false distinction between "believers" and "rationalists". The trickle-down Dawkins effect has got millions of people thinking that faith is ignorant and childish, with atheism the smart and logical position.

I interviewed the comedian Miranda Hart recently. She told me she believes in God but was nervous of being quoted on it.

"It's scary to say you're pro-God," she said. "Those clever atheists are terrifying."

"Oh, nonsense," I said. "Let them tell you it's stupid to believe in something you can't explain. Then ask them how an iPad works."

Atheism itself is fine; good luck if that's what you sincerely (don't) believe. But the proselytising, fundamentalist new atheist movement sets itself up as more "logical" than faith, which is ridiculous. Given the incomprehensible scale of the creator we'd be talking about, the only "logical" position is agnosticism.

So why do the proselytisers fight so hard to be right? In place of the comfort which faith can provide in the face of death, grief or loneliness, they offer… nothing. They are suspiciously eager to snatch away the consolations of their fellow men.

Why? Because they think religion causes violence? Human nature contains a streak of fear, greed, selfishness and territorialism that must result in a mean level of dissent and bloodshed, with or without the excuse of religious difference. Without religion, human life is no longer sacred – nothing is – so it's not "logical" to believe we'd be gentler if it disappeared. All we'd have to replace it is a trust in altruism, which is certainly no less naive than believing in God.

So what would that leave, as a moral framework? The law? Do google "Twitter joke trial" before you throw our future behind that.

Or is it because some religious arguments are misogynistic or homophobic? Believers can still argue back.

It is not "logical" to imagine that faith could disappear anyway. It is natural to seek hope beyond the trials and finity of existence. If the big religions were destroyed, humanity would simply invent new, smaller, madder ones. Thousands of them. The man who attempts to argue both that religious difference causes violent bloodshed and that the big faiths should be dismantled is therefore being short-sighted, obtuse and not very clever.

Unfortunately, there seems to be no serious intellectual resistance. Last weekend, there was a huge religion v atheism debate in Canada. On the sceptics' side: the brilliant, witty, fast-thinking author Christopher Hitchens. On God's side: Tony Blair.

Terrific. That was hardly a match-up to challenge the idea that non-believers are rationalists and the faithful are self-righteous cranks with mad, starey eyes. You'd be better off sending in Gillian McKeith.

Come on; let's make this a fair fight, at least. Identify yourselves, thinking believers! Don't be cowed into silence by the idea that faith is the weakness of a halfwit, like buying your goldfish Christmas presents or watching ITV2. It isn't.

I'll start: I believe in God and I'm perfectly intelligent and rational.

Not that you'd think so if you saw me at Lambeth Palace on Wednesday night.

"I carried a watermelon"?

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