I’m beginning to feel a bit sorry for older women. You’re being somewhat unfairly portrayed. Every few weeks since the Weinstein allegations broke, kicking off a movement – #MeToo – against harassment, abuse and sexual violence that shows no sign of abating, some older woman or other is brought in to tell anyone who will listen how stupid the whole endeavour is.

The impression building is that women of a certain age – our mothers’ and grandmothers’ generation, and often those younger, too (basically anyone who can’t be dubbed a “millennial”) – think this movement is daft, that we are whiny weaklings complaining about nothing, that we scream harassment and abuse in a hand grazing a knee. But this is patently not the case. There has been cross-generational support for #MeToo; it’s been moving to see. We owe much of today’s feminist work to you, the women who came before us.

The latest older women to take issue with #MeToo is Germaine Greer, who can always be relied on for a soundbite on just how badly she feels pathetic younger woman are doing feminism. In the interest of full disclosure, she once wrote a nasty review of The Vagenda, the book I co-wrote, and author Laura Bates’s book, Everyday Sexism.

Aside from containing quite a few factual inaccuracies that letter writers to the New Statesman were happy to correct on our behalf, particularly with reference to female biology, it also witheringly dismissed the role of social media in modern feminism. “Unpacking your heart with bitter words to an anonymous blog is no substitute for action,” she wrote, of the Everyday Sexism project. This is almost exactly the same line that she has taken with #MeToo. The words she used to describe me and my fellow young feminists, that we were merely “shrieking” and “bitching” and “whingeing” were revealing. It made me wonder if Greer actually likes women, particularly young women, at all.

Greer makes the mistake of viewing the internet and the activism which takes place on it as distinct somehow from real life, when most of us know, regardless of age, that it is not somehow magically separate, but simply one part of it. #MeToo may be an online movement, but it is having real-world consequences, just as in the same way the work of The Vagenda and Everyday Sexism’s was not limited to Twitter.

Greer makes the mistake of viewing the internet and the activism that takes place on it as distinct from real life

We spent days and days doing outreach in schools and universities, a lot of it unpaid, providing consultancy to a range of organisations, and even meeting with politicians. Similarly, #MeToo has seen women gather the courage to approach their HR departments, setting up their own organisations, joining unions, forming legal funds to help women sue their abusers, taking to the streets in protest, and a hundred other things besides. It has galvanised women across the world. To reduce it to whining is actually rather sexist.

It’s sad that women like Greer, Catherine Deneuve, Brigitte Bardot, and Donna Karan do not get it. And it’s sad that the establishment relishes their input to such an extent – for who better to tear down a mass of women in revolt than one of our own? But they should not be taken to be representative. Those women who seek to frame the new feminism as a bunch of clueless snowflakes, offended at every come-on seem to share little in common attitude-wise with so many older women that I have met. Because what some forget is that these generations – these mothers and grandmothers and colleagues and mentors and teachers – well: you raised us.

You brought us up to be this way. Whether you mothered us or mentored us or wrote books we read, it is you who passed on to us that hard-learned but fervent hope that we young women deserve to walk through life without fear of abuse, harassment, and discrimination. You taught us that men would try and put their hands on us. You taught us how to fight and to speak up, and not take it lying down. We did not pluck these ideas spontaneously from the ether. #MeToo is merely another kind of consciousness-raising, and you pioneered that decades before we were even born. This is not a case of young versus old, because you women who came before planted the seeds. Some of you have resisted this collective spirit, taken the hardened attitude that you weathered the storm, so why shouldn’t we?

But more of you, such as Suzanne Moore writing in the Guardian earlier this week, have been on board. Attitudes have changed, of course, attitudes are changing all the time. But credit where it’s due: women like my grandmother, and like many of you reading this, have always said that sexual harassment was unacceptable. It’s just that no one is interested in putting my grandmother on the Today programme (which is a real shame, she would make short work of John Humphrys).

It’s ironic that so many of these supportive women, our feminist forebears, will have been influenced by Greer, who now seems to want to disown my generation’s brand of feminism. It is a shame. #MeToo has had a profound effect on me, has changed my life really, and the same can be said for many others. That’s thanks to our elders and also, regardless of where she’s at now, thanks to Greer’s historic work. Like it or not, Germaine, we are your legacy, and we’ll keep on fighting. It’s a shame you’re not onside but well, thankfully, there are many more where you came from.

• Rhiannon Lucy Cosslett is a Guardian columnist and author