She was asked how she felt about the way the media covered her pregnancy two years ago, and also about the stories questioning the ability of the pregnant MP Rachel Reeves to do her job. "I'm furious," she said. "How in 2015 are we still having a discussion about whether pregnant women can do their jobs properly?"
Swinson was speaking at the first Omniwomen UK training day for 170 rising female stars across Omnicom's companies and ahead of Sunday's International Women's Day.
Swinson said she suffered more from ageism than sexism at the start of her political career. She was 25 years old when first elected and nicknamed the "baby of the house". "I always hated it," she said, because it was such "an infantalising title".
She added: "I had the dual issue of being a woman and being young. I think I experienced ageism more than sexism. I used to get mistaken for a researcher all the time because people looked at me and didn't see an MP."
Swinson told a story about canvassing for support at people's front doors when she was 23 and trying to get elected. On one occasion, she did it without wearing make-up and people's first reaction was to remark how young she was. So she made sure she wore make-up the next time.
She also spent her early twenties trying to look like she was in her thirties: "I always wore a suit. I didn't want people to question whether I could do the job."
It took Swinson a long time to realise that she had to ask to become a minister. "I thought I'd do a good job and then I'd get promoted," she said. "It took me a while to realise I had to go and make the case."
People often make fun of ideas they are threatened by, Swinson added.
At a recent debate on care, Swinson was discussing the role of men in society and, at one point, said that boys should be able to play a nurturing role and that it was OK for them to play with dolls. According to Swinson, The Sun took that quote out of context to say she thought all boys should play with dolls.
"People deliberately ridicule an idea to trivialise the issue. People feel threatened by it," she said.
But Swinson added: "Gender equality doesn't happen by accident, we have to make it happen. We need to get an equal distribution of power, then all the other issues can be dealt with as well."
The Omniwomen day focused on a range of themes that had been identified as important for Omnicom's female staff including gender codes, confidence, resilience, leadership and motherhood. The event was launched in the US a year ago.
As Cilla Snowball, the group chairman and group chief executive of Abbot Mead Vickers BBDO, said in her introduction: "This is not about men-bashing. It's a positive starting point – we're all in this together."
The day included an all-male panel of agency leaders discussing their views on agenda. PHD's chief executive, Daren Rubins, said that before his current agency, he had worked at a range of companies where there was an "aggressive, masculine culture" for male bosses.
But since joining PHD, where he has had female superiors, the working culture has been far more open, warm and collaborative, encouraging self-awareness. Rubins believes that differentiates PHD as a business.
Ije Nwokorie, the global chief executive of Wolff Olins, said: "We need to redefine leadership and change our icons. We need to move away from the Steve Jobs/Alex Ferguson approach. A leader's role is to equip more people to succeed."
He suggested that big roles be split so more people can lead different parts of a business rather than the expectation for one person to do everything in a traditional pyramid hierarchy. That way, people wouldn't get promoted away from what they are good at – and enjoy – doing.
Nwokorie also said there was a danger of making it entirely an individual's responsibility to succeed, including when it comes to matters such as pay rises: "We have to get the principles right. We should be making sure we reward people on how well they do their jobs so they don't have to ask."
He added that companies needed to create a culture where people felt empowered to call out any sexism they saw in their jobs.
Rapp's UK chief executive, Marco Scognamiglio, said that, to be a leader, people needed confidence and self-belief because it is a tough, often lonely, gig. "You have to be really passionate about what you do so your energy can carry you through," he added.
In stressing the importance of diversity in leadership, Omnicom Group's executive vice-president, Janet Riccio, said: "This is not solely a women's issue, but rather a strategic business imperative.
"Companies that have diverse, inclusive management teams and boards financially outperform those that don't. The best investment we can make is our own human capital."