The estimated 2 million protesters who took to the streets across more than 60 countries this weekend are right to battle the threats to historic advances in equality

It is not by chance that women have led the opposition to Donald Trump’s ascendancy. An estimated 2 million demonstrated across the United States and around the world this weekend, in events across 60-plus countries, including Malawi, Peru, India and Lebanon. Attendance in Washington DC was estimated to be three times that of Friday’s inauguration. In London, up to 100,000 marched. Even Antarctica saw a protest.

Marchers were driven by more than visceral disgust at a commander-in-chief who has bragged about sexually assaulting women and denigrated them in the crudest terms. Mr Trump has said that women should be punished for abortion and, though he later rowed back on that, has said he will appoint supreme court judges who oppose Roe v Wade, sending the issue back to states. His impact will not end at US borders. He is expected to reintroduce the “global gag” rule, which denies family planning funding to foreign groups using even their own money to advise women about abortion. Crude US protectionism could push low-paid female workers overseas into outright destitution. So while women welcomed male participants, they organised in the understanding that their lives and bodies will be affected disproportionately.

Mansplaining dismissals of the protests have missed the point. Democracy does not stop at the ballot box, any more than activism ends on the streets. Participants understand that these marches began a long struggle, which will need to take many forms and to be expressed at the highest levels of power (Theresa May, so cagey when asked whether she would raise concerns about his “unacceptable” comments on women in their meeting this week, should take note). And it is, in fact, Mr Trump who promoted and relied upon identity politics in this election.

Women’s rights are simply human rights; human rights are women’s rights, the marchers reminded us – a saying popularised by Hillary Clinton, then first lady, at 1995’s UN world conference on women. The Beijing declaration reached at that meeting was the most progressive international agreement on advancing women’s rights. Many fear that the global community is now going backwards. Human rights groups warn that in international policy-making, countries are increasingly pushing back against gender equality and sexual and reproductive rights.

The world has many Trumps: bullies, sometimes great of power, but mean in character and vision. In Russia – where more than 10,000 women a year are believed to die due to domestic abuse – parliament is currently considering decriminalising “moderate” domestic violence. In Bangladesh, which has one of the world’s highest child marriage rates, the government wants to permit the marriage of girls under 18 in “special cases”.

Women are punished not only by regressive policies affecting them as women, but also those that affect other aspects of their identities. In the UK, experts estimate that austerity will have hit women twice as hard as men by 2020, and less affluent women the hardest, thanks to tax and benefit changes. That’s setting aside the cuts which are closing refuges, for example.

Against these daunting challenges are ranged what Mr Trump would call Nasty Women, who believe they have a right to do more than please and comply. They are many. After initial criticism, march organisers promoted broad agendas including issues such as migration and disability rights and mass incarceration. Women’s movements have of course made mistakes, sometimes bad ones. But to portray feminism as a hobby for myopic, white middle-class ladies – like needlepoint, but angrier – misunderstands both a history starred by Sojourner Truth, Annie Kenney and Huda Sha’arawi and the present movement’s dynamics. While 53% of white female voters backed Mr Trump, 94% of black and 68% of Latino women supported Mrs Clinton. Establishing a degree of unity among his opponents will probably be easier than engaging those who chose him.

There is some good news amid the gloom. In places, resistance by women is already reaping results: in Poland, mass demonstrations saw off an attempt to introduce an almost total ban on abortion; in Chile, the senate will soon vote on President Michelle Bachelet’s proposals for exemptions to the abortion ban. Mr Trump’s victory demonstrates that advances can be undone, and doubtless will be over the next four years. But with sufficient thought and determination, setbacks can be reversed, too.