Serena Williams is a warrior. Even people who know next to nothing about tennis know that; we’ve all read about how she bounced back from almost dying giving birth to her daughter Alexis Olympia, to playing tournaments six months later. She is astonishing, extraordinarily talented, the greatest player of her generation.

But she is also, it seems, fighting a very different battle off court. Days after being thrashed by the British player Johanna Konta, Williams wrote on Instagram that she had been worrying about “not being a good mom” and was still processing “postpartum emotions” that she hints have affected her game. She described her conflicted feelings about an intense training schedule that means she’s not with her daughter as much as she’d like, in terms that many new mothers returning to rather less high-profile jobs will recognise. What had been a straightforwardly uplifting fairytale – woman has baby, comes back even stronger, and in the process shows everyone that motherhood doesn’t have to take it out of you – is becoming more complicated. We’re now seeing a more vulnerable side of Williams, as she concedes that in some senses motherhood has changed her; that her astonishing physical strength sometimes conceals psychological turmoil.

It is a difficult moment for her. But it’s also where her real steel shows through. There was bravery in Williams’s return to court and she deserves all the plaudits for it. But there’s a different kind of bravery in being willing to admit to any kind of weakness, particularly for an athlete who knows her opponents will be scrutinising her for any chink in the armour. And it takes significant courage for women in the public eye to be honest both about the trade-offs all working parents secretly agonise over, and defiant about their determination to carry on nonetheless.

“It’s totally normal to feel like I’m not doing enough for my baby,” Williams wrote, noting that both working and stay-at-home mothers worry sometimes about doing the right thing by their children. “I’m here to say that if you’re having a rough day or week – it’s OK – I am, too!” The added pressure for her, of course, is that she’s doing it in front of millions and in the knowledge that she has become a much-needed role model for young black girls in particular.

It would be wrong to reduce Williams’s entire sporting career going forwards to a story about motherhood. All athletes have ups and downs, and not every lapse in form over the years will be explained by what’s going on in their personal lives. But her speedy comeback undeniably had a particular resonance for working women in America, where there’s still (astonishingly) no universal right to proper paid maternity leave and many mothers have no choice but to return to work very early by British standards. The risk Williams is taking is that some women may feel disheartened to learn that she is human after all, while others may even crow; see, motherhood does take it out of sportswomen after all! She is walking a difficult tightrope between inadvertently giving ammunition to her critics, and simply being honest.

But many women will feel nothing but relief to know they are not alone, that there isn’t something wrong with them if they can’t bounce back instantly as if nothing had happened. Like the singer Beyoncé, who admits in the current edition of Vogue that in retrospect she put too much pressure on herself by going back on tour three months after the birth of her first child, Serena Williams has given ordinary women permission to be kinder to themselves. Bodies don’t just snap back instantly after childbirth, and nor do emotions. Both women have done us a favour by saying so.

• Gaby Hinsliff is a Guardian columnist