When Andrea Leadsom’s comments about motherhood and Theresa May, in an interview with the Times, first emerged on Friday evening, her supporters cried foul and demanded to see the transcript. When the transcript was published, they demanded the newspaper release a recording of the exchange.

It was hard to see what Team Leadsom, in its escalating indignation at actual words spoken by their candidate auditioning to be prime minister, would ask for next. The ability to turn back time to ensure the interview never happened, perhaps?

In fact, the audio version of Leadsom’s remarks surely only damned her further, because of her very audible emphasis on the word “children”: “She [May] possibly has nieces, nephews, lots of people, but I have children, who are going to have children, who will directly be a part of what happens next.” To compare herself with her leadership rival, who only a week ago spoke of her sadness at being unable to have children, was the height of cruelty, even with her earlier qualification that she did not want to set it up as “Andrea has children, Theresa hasn’t”.

As if that wasn’t nasty enough, she turned this difference in fortunes, this cruel randomness of the fertility lottery, into a CV qualification more embellished than her City background. Being a mother, Leadsom claimed, means “you have a very real stake in the future of our country”. This is a ludicrous and hurtful assertion, because the corollary of this argument is that May, and other childless people like her, do not care about what happens to the economy, or if hospitals close or school standards fall. It implies that they are of less value to the country, without their 2.4 “stake” in society, an only-in-it-for-themselves, can’t-take-it-with-you army draining the nation’s wealth and shrugging at the pound collapsing.

This argument is clearly wrong, but it goes to the heart of our society’s fetishisation of motherhood. There has been a misplaced emphasis on the “mumsnet vote” at the last three or more elections, as if fathers and adults with no children don’t care passionately about the NHS, the economy, or having a job. Politicians believe in the potency of motherhood, which is why Leadsom mentioned her own status so many times during the referendum. Three years ago Tim Loughton, the former education minister, apologised to his ex-colleague Sarah Teather for saying she “doesn’t really believe in family” because she “didn’t produce one of her own”. (It is worth pointing out that Loughton is Leadsom’s campaign manager). Last year, during Labour’s leadership contest, Yvette Cooper, a mother of three, was accused of playing up her family experience against her childless rival Liz Kendall – although, unlike Leadsom, Cooper spoke only of her own situation, rather than comparing it to Kendall’s.

Mothers – and I speak as one of a five-year-old – jealously guard our territory, luxuriating in our insufferable martyrdom, boasting of being able to wash a PE kit while sending an email to the office. This is not to say working mothers have to balance work and home life, and the financial pressures of this can be extreme. But we do not have a monopoly on juggling, or worrying about the future, or playing a part in civic society. In fact, there is a perfect example of someone who has devoted her working life to public service, who has juggled constituency work, red boxes, parliamentary votes, and, in recent years, managing her diabetes. Her name is Theresa May.

Being a mother – or father – changes your perspective but it does not make you any fitter to be prime minister. A politician does not need to have a career in the City to make a good chancellor, just as the job of environment secretary does not require a background in farming. Has being child-free made Nicola Sturgeon a less effective, less skilful first minister? Of course not. Has Angela Merkel, one of the most powerful leaders in the world, been unable to have “perspective” on all the troubles of the EU because she is not a mother? It seems laughable to suggest this is the case.

Judging by the reaction on Twitter, Leadsom’s remarks appear to have done her campaign real damage. The home secretary’s response has been dignified, issuing a tweet urging her rival to sign up to a “clean campaign pledge”. The contrast between May and Leadsom seems stark. Yet, as David Cameron pointed out last year, Twitter is not Britain. And it is certainly not the Conservative membership who will decide this contest.

As indignant and outraged Leadsom and her team are at being splashed across the front page of the Times, her comments were at the heart of her pitch to the Tory grassroots. This was not so much a dog whistle but the loud booming voice of a town crier in the shires. Leadsom knows that many Conservative members will see themselves reflected in her: Christian, socially conservative, anti-gay marriage, Eurosceptic.

Female Tory MPs speak of how they are still asked at selection interviews about husbands and children. But there is more: post-Brexit, the conditions are right in the Conservative party for a Corbyn-style insurrection of grassroots members against the modernised, centrist, bureaucratic top of the party and its MPs.

May has talked tough on immigration and her cautious, barely noticeable role for the Remain campaign in the referendum was designed not to spook the Tory rank and file. But the risk for the home secretary is that she nevertheless represents, to members, a bureaucratic, authoritarian politics that many of them have just voted against. Leadsom is a traditional Tory but with a fresher, insurgent agenda, vowing to invoke article 50 to trigger Brexit negotiations as soon as she becomes prime minister.

Last week, she came top in a survey of activists for the ConservativeHome website. The more Leadsom and her allies rail against the Times, the Remain-supporting beacon of the establishment, for orchestrating what they claim is a “metropolitan stitch-up”, the greater her appeal among the restless Tory membership will be.

As well-intentioned as her warning was, back in 2002, that they were seen as the “nasty party”, May could pay the price next month. Because as nasty as Leadsom’s remarks about were, they will register among traditional Tories. Leadsom has been called naive for falling into a “trap” of talking about motherhood. In fact she has been anything but.

@janemerrick23