Cathy Newman and Caroline Lucas are locked in a clash over plans for the Green MP to job share the leadership of her party, raising questions about how women see their evolving role in the workplace.
Newman, a presenter on Channel 4 News, had accused Lucas of making women MPs seem "weak" and "riddled with self-doubt" for announcing her intention to share the role of Green party leader if elected.
When Lucas first announced that she would run to be co-leaders with Green work and pensions spokesman Jonathan Bartley, she explained it was important she was able to work effectively as a local MP, adding that going it alone in a leadership role was "not something that would sit well with that".
But the move was derided by Newman, who said that while job sharing could "work perfectly in another setting", it was not true of Westminster.
"This smacks of classic feminine self-doubt," the broadcaster wrote in the Telegraph.
"What man would make the same admission?
"He’d call for back-up, or a bigger office – but still demand the title and the sole claim on the top job.
"I fear Ms Lucas is making a mistake if she equates an appetite for a less tribal politics with leadership by committee. At a time of such public cynicism about our elected representatives, strong, brilliant leadership is needed now more than ever."
But the Brighton Pavilion MP hit back at the claims, saying her decision was nothing to do with self-doubt and that in fact it took self-confidence to admit that you "can't do it all".
She pointed to her co-leader-hopeful, Bartley, and said his reasoning for wanting to share the job was because of caring responsibilities at home.
“I have a huge amount of respect for Cathy Newman, but she’s got this one wrong," Lucas told The Huffington Post UK.
"For starters she assumed that I was alone in seeking a job-share – thus writing Jonathan Bartley out of the story.
"In fact Jonathan approached me about co-leadership because he, like me, has a vision for leading the party, but because of caring responsibilities at home he wouldn’t be able to commit to the job full time."
Lucas, who led the Greens before their current leader, Natalie Bennet, took over in 2012, also said she wanted to see more MPs job share, in a move that would make performing roles in Parliament "far more possible for far more people".
She said: “If Cathy had asked me why I’m going for this job-share then she’d have found that self-doubt isn’t the problem. Indeed I would argue that it takes a degree of self-confidence to admit that you can’t do it all and are willing to share power.
"Of course politics is about leadership – but a single figurehead isn’t the only way. We need to crack open our current closed political system and ensure that a far wider diversity of voices are heard.
"That’s why the Green Party has also been championing the idea of job-sharing MPs - making the job far more possible for far more people.
"Being alone at the top isn’t the only way to lead - and through our co-leadership we’re hoping to show that another way of doing things is not only possible, but beneficial for all involved."
Lucas' push for more MPs to share their jobs comes after a senior Conservative MP attacked parliament’s “default no position” on a legal change that would allow MPs to job-share with another person.
Chair of the health select committee Sarah Wollaston told HuffPost UK last year that it should be “perfectly possible” for two people to combine their candidacies to encourage more women and a greater variety of people with different experiences to become MPs.
Dr Wollaston, who took part in a job share as a GP before she entered Westminster, was reacting to news a court had barred two women from standing together as Green Party candidates in the May election last year.