It's an outright throaty laugh and it made me cry. I never thought I'd hear her sound like that again, because I'm still not ready to laugh. It's been nearly a year since deranged America elected its orange popinjay and, when I see or hear President Donald Trump, I still feel a little sick. If you're Australian, please don't trouble me with your opinions about the United States electoral system. I prefer our system because we at least get the government we deserve.

Anyhow, she's laughing and I am transfixed. She's talking to Jon Favreau of Crooked Media, who was director of speechwriting for president Barack Obama from 2009 – and she's relaxed. She's had time to think about what happened and, happily, that's also the name of her book (What Happened?). She's spruiking it on Pod Save America, a strange ramble among mates who love the Democrats. I'd say it's an insiders' view of the way in which the Democrats are coping with the election result – it's not always great listening but I learn something from each episode.

I bought Clinton's book on Saturday straight after listening to her episode because I needed fuller answers immediately. Whatever she says matters – not just for Americans and American women, but for all women.

What's striking is how her response has so much in common with the one Julia Gillard gave when she was replaced by Kevin Rudd. Gillard said: "I do want to say about all of these issues, the reaction to being the first female prime minister does not explain everything about my prime ministership, nor does it explain nothing about my prime ministership ... [the way she was treated as a result of her gender] doesn't explain everything ... it explains some things. And it is for the nation to think in a sophisticated way about those shades of grey. What I am absolutely confident of is it will be easier for the next woman and the woman after that and the woman after that – and I'm proud of that."

Clinton says more or less the same. Favreau tells her that, since she lost the election, a record number of women have decided to run for office. He then asks her what advice she would give them. Clinton says it's important to discuss the issues of sexism so "they won't have the same impact on the next election and the one after that". In her book, she writes: "This has to be said: sexism and misogyny played a role in the 2016 presidential election. Exhibit A is that the flagrantly sexist candidate won. A whole lot of people listened to the tape of him bragging about sexually assaulting women, shrugged, and said 'he still gets my vote'."

I spend less time on social media than I used to, partly because it's become a playground of derangement. Even normally sensible people lose self-control when discussing politics. I've made a few errors there myself and realised it was the company I was keeping. But there's another reason I spend less time there: it's a place for torrents of misogyny, a phrase I borrow from HuffPost Australia's editor-in-chief, Tory Maguire.

And it's on social media that we see it play out: the endless, photoshopped images, where women are victims of violence. The vile language. The complete diminution of public discourse. Over the weekend, Trump retweeted a doctored image that showed him hitting Clinton with a golf ball. And while thousands of people responded with condemnation, more than 60,000 people "liked" the tweet. Maybe some were just using a "like" to bookmark the imagined violence. Maybe.

A small thing, you think? It's how often one needs to deal with it that makes it different for women. As Clinton writes: "Just look at the [comments] when a woman dares to voice a political opinion or even just share an anecdote from her own lived experience. People hiding in the shadows step forward just far enough to rip her apart."

But we know all this. When women run for election in Australia, they also cop this level of vitriol, which is enough to make some think twice about standing for any elected office. It's never about their policies. It's about their bodies and their personalities. As Clinton says, when a woman lands a political blow, she's construed as a "nasty woman".

And what does it mean when we choose people – men – who are less capable, much less capable, over those nasty women?

Buy the book. It doesn't explain everything. It explains some things. And that may ease the grief.

Jenna Price is a Fairfax Media columnist and an academic at the University of Technology Sydney.

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Twitter: @jennaprice