International Women's Day 2015: Celebrating the whirlwind wit of feminist Simone de Beauvoir

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It is probably fair to say that I approached Simone de Beauvoir the wrong way round: I visited her grave before I read a word she'd written. This was not particularly my intention. Many years ago I was in Paris, with a handsome man who liked Sartre (my youth was filled with such men, several of whom also played the guitar. I have nothing to offer in my defence). He liked Sartre so much that he wanted to visit the great man's grave.

Sartre was a bit recent for me, philosophically speaking: in those days, I had recently graduated in classics, so I knew a reasonable amount about Plato and Aristotle, but very little about philosophers after, say, Marcus Aurelius. But since we'd already been to the Louvre to see a bust of Socrates, it seemed only reasonable to head to Montparnasse Cemetery to check out one of his most celebrated descendants. And when we arrived, of course, I realised we were actually visiting two of them.

Sartre and Beauvoir share a headstone, an austere block with plain lettering. Just their names and dates. Him above her, because he died first. From a distance, it looked like it had been vandalised, or at least littered. A few dying flowers lay limply across the grave. But they were surrounded by paper scraps and pebbles, as though dozens of people had emptied their pockets and left the contents behind. As we drew closer, it became clear that it was covered with notes – which made perfect sense: people often write messages to authors, and death is no obstacle to that – and Metro tickets, which made no sense at all. I asked the handsome man why people left their tickets on this grave, weighed down by small stones. He didn't know either.

It was surprisingly difficult to find the answers to such questions in the days before search engines. And once I got back to the UK, I forgot about it. I didn't think of it again even when I finally read Simone de Beauvoir. I only remembered it when I started writing this piece. A quick online query provided the answer, or at least one answer. Apparently, people leave the tickets to commemorate the couple's support of the French Maoists, who once gave Metro tickets away after a hefty price hike rendered them unaffordable to many ordinary workers. One source explains that Sartre even edited the French Maoist newspaper for a while, when the usual editor was arrested.

So the tickets – which are still piled on the grave today – are a neat symbol of Beauvoir and Sartre's socialist ideals, far more than weary carnations and dead roses. Although I find myself wondering if all the ticket-leavers know this backstory, or if some just place their tickets on the gravestone because they see that other people have done so. I can't now remember if we left our tickets there in similar vein, or retained them for the journey back to our hotel.

When I finally got around to reading The Second Sex, I knew that – had I read it before that Parisian trip – I would have left her a note and a book of train tickets. I knew it from the first two sentences: "I hesitated for a long time before writing a book on woman. The subject is irritating, especially for women; and it is not new." That's an audacious way to begin your masterwork. And this witty, astringent tone pings throughout Beauvoir's writing.

No wonder, when you consider who she was reading. On the second page, Beauvoir quotes one of my favourite lines from Dorothy Parker: "I cannot be fair about books that treat women as women. My idea is that all of us, men as well as women, whoever we are, should be considered as human beings."If I had to summarise my own feminism, it would boil down to this: women are the same thing as people. That's it. They aren't a weird, incomprehensible sub-group, they're just people. This is why Freud's ponderings on what women might want have always annoyed me: women don't all want the same thing any more than men do. Why on earth would we? We're not members of some bizarre cult, we're just people. So we tend to want the same thing as some other people would want. In this particular instance, I wanted to go on reading The Second Sex, because it's hard not to like someone who likes the same bits of Dorothy Parker as you do.

We're so used to seeing austere photographs of Beauvoir, her eyes slightly hooded and her mouth set in a straight line, as though she was thinking high-minded thoughts about a complicated thesis. She was half a head taller than Sartre, and she had the slight stoop of a woman who didn't want to use her height to intimidate. Why bother, when you had a brain that could crush a person without breaking a sweat? But there are a couple of pictures of her where she was caught in a less formal pose, and a smile rearranged her features. The hooded eyes crinkled with merriment and – in her later years especially – there was something joyously expectant about her. It reminds you that she had she was probably a lot happier than Dorothy Parker, even if Parker was funnier.

And Beauvoir could flit between high-minded philosophy and a pointed remark without any trouble at all. Rebutting an article by Claude Mauriac "whom everyone admires for his powerful originality," she observes: "Clearly his female interlocutor does not reflect M. Mauriac's own ideas, since he is known not to have any." Ouch. It's only on reading the second sentence that you realise just how ungenerous she was being in the first. Everyone else may admire Mauriac, but you are left in no doubt that Beauvoir disagrees, and that she could give you eight perfectly formed reasons for why everyone else is wrong.

There is something dazzling about the certainty Beauvoir can bring to almost anything, from pseudo-biological determinism to the seclusion of women in ancient Athens. She is an expert in her subject, and she makes no apology for it. Only when you read her do you realise how many women write using a default uncertainty – maybe, perhaps, possibly. I do it myself: look at how I began this piece. "It's probably fair to say…" I'm writing about my personal experience, so it isn't "probably fair", it's actually the case. Yet still, I cannot resist adding a layer of ironic distance between me and my words – between my writing and your reading – which imparts a faint sense of doubt. I mean what I say, but I don't want to blare it out, like a spotlight. I place my argument in front of you, preferring you to come across it for yourself. Beauvoir shines her words into your face until your eyes water. It scarcely needs saying that you wait a long time to read the word "maybe" in The Second Sex.

It should be disheartening to read this book now, and realise how little has changed since it was first published. "Misogynists have often reproached intellectual women for 'letting themselves go'; but they also preach to them: if you want to be our equals, stop wearing make-up and polishing your nails." If Beauvoir was calling out the double standards applied to women in 1949, how are we still having to live with them today? "The woman… knows that when people look at her, they do not distinguish her from her appearance: she is judged, respected or desired in relation to how she looks."

But I prefer not to be disheartened. We've achieved a lot since 1949. We're still a long way off equality, but we're travelling towards it, even if the journey includes occasional back-sliding. Beauvoir never resists drawing parallels between racism and sexism, and the world hasn't stopped being racist yet, either. Still, things are better than they were in 1949. Reading The Second Sex is like having someone cleverer and more articulate than you remind you that you aren't paranoid. It is difficult working in a field where there aren't many women. It is annoying that you are sometimes given a choice between being considered a slattern (no make-up, sensible shoes) or a bimbo (polished nails, nice hair). Articulate it, and you're more likely to notice it and fight it, for yourself and for other women, too.

"Throwing oneself boldly towards goals risks setbacks; but one also attains unexpected results," writes Beauvoir. "Prudence necessarily leads to mediocrity." It's advice than we should all bear in mind. No one wants to fail, but we all do sometimes, and it is undeniably better to fail at something difficult and risky than at something easy and safe. Besides, if there is a single skill which will get you through life above all others – more important than cleverness or passion or imagination – it is resilience. Without it, even the most brilliant person can be crushed. And no one can develop resilience in a vacuum. You have to fail in order to learn how to recover from failure.

There are plenty of people who dislike Beauvoir, because she was angry. Anger, of course, is not considered a virtue, and nor is it ladylike. But anger can be intensely powerful: how would anyone fight injustice without being angry that it exists at all? There is a difference between anger – which can be clean and pure – and petulance. The latter makes us petty and mean-spirited, interested only in our own advancement and not in that of others. But life isn't a zero-sum game. There isn't a limited quantity of success or happiness, meaning that if one person achieves something, the rest of us take an automatic step backwards.

So, if you decide to read Beauvoir on International Women's Day, I would remind you that while anger may not be very ladylike, neither was she. Nor am I. And, hopefully, neither are you. And that's not a bad thing at all. Anger doesn't preclude joy or happiness, it exists in us alongside those emotions, ready for when we need it. It's perfectly reasonable to be angry when you're on the receiving end of an injustice, and it's equally sensible to be angry when you see anyone else having an unnecessarily difficult time. Nothing changes unless we get angry occasionally: if the suffragettes hadn't been furious about the injustice of their situation, we might not yet have the vote. And if it isn't ladylike to get angry, that's fine. I'd rather be a woman than a lady, any day.

Vintage Feminism: classic feminist texts in short form are out now (Vintage Classics, £4.99)