Lots of friends are furious about Jeremy Corbyn. As lifelong Labour supporters they're gutted to have an unelectable leader. But I'm energised. It feels like the end of the political ice age. Some sort of political spring seems to have broken and people long bored by the Westminster status quo are waking up.

He reminds me of being 16 and arguing politics with my working-class-done-good Tory dad. Why can't we care about people, why can't we have a fabulous education system and health service, why do we have spend so much on arms? I can picture my dad rolling his eyes at my naivety about "the real world" before we threw ourselves into a huge row about the evils of Thatcher and the poll tax.

Jeremy Corbyn
Jeremy Corbyn on his way to his first PMQs as Labour leader on 16 September Getty

Watching Corbyn on PMQs this week was like watching your favourite aunt take on a pack of Rottweilers. You admire her spirit and wish her well, despite the odds. And disagree with her on almost everything.

I love his determination not to be bullied. He won't wear a decent suit or sing when he doesn't want to or spout platitudes he doesn't believe in. He won't put a woman into a top job because that's what you're supposed to do to avoid flack. He talks to the groups he is not supposed to talk to. He says that he won't make the concessions that could get him elected as prime minister.

Obviously for Labour, the apparent Catch 22 is frustrating: his biggest attribute is his refusal to change, the only way to make him electable is for him to shift. So I've been calling pollster friends all week and asking what would it take for him to become prime minister.

To which they shake their heads in confusion and say he just can't. To quote Keiran Pedley at GfK: "To win in 2020 Labour would have to put together a grand coalition of Ukip, SNP, Green and Lib Dem supporters while raising turnout in a wholly unprecedented way. Personally I am looking forward to the policy platform that unites SNP and Ukip under the Labour banner..."

Andrew Gunn, reputation specialist at Populus, says much the same, adding: "He'd need external factors: infighting within the Tory party over their next leader, serious Tory mismanagement of the economy (particularly rapidly rising interest rates) and another scandal that makes MPs expenses look like mild over-exuberance; and the abolition of the first-past-the-post system. Oh, and a keenly applied razor."

But maybe we're all asking the wrong question; maybe the point of Corbyn is that he never will be the right person to be PM. Perhaps his gift is to humanise politics by making our other political leaders look sweaty, plastic and heartless in contrast. Maybe his role is to remind us what we used to believe in before the real world cluttered the picture. Was it me or did Cameron seem less guarded and more human this week?

Christine Armstrong is a contributing editor of Management Today, author of Power Mums (interviews with high-profile mothers) and founder of www.villas4kids.com. She can be found on Twitter at @hannisarmstrong.