MY older daughter was born just after 10pm on June 26, 1996 (four minutes after Germany knocked England out of Euro 96, I remember; not that I saw the game).

My second daughter was born five years and four months later (almost to the day). I have been a father for more than 17 years now. But if I'm totally honest I'm still a little fuzzy on the job spec.

I get the basics. I understand the need to provide food and clothing and shelter. I was fine with the nappy-changing, the walking around singing to crying babies in the middle of the night. I get the importance of encouraging them to realise that pizza and chips is not really a healthy diet (even if now and again - or maybe slightly more often - I do indulge them), and making sure they go to school and do their homework; and reminding them that they live in Scotland, not Spain, so really should consider putting a coat on sometimes; and driving them around to sleepovers, acting classes, activities ... I've got all that nailed down.

But that's just fatherhood 101, the kind of stuff you'd find on page one of The Bluffer's Guide To Being A Dad. Bare-minimum parenting. Basic duties. What about the bigger picture? How do we equip our daughters to venture out into the 21st century? How do we prepare them to deal with sexism, misogyny, the cultural and social pressures that tell them they should be thinner, work harder, own a designer bag (or three)? How do we encourage them to speak up for themselves, be unafraid to fail, find their own measure of success, and maybe learn how to cook something for dinner if no-one's going to do it for them?

And I'm guessing that the answer "Ask your mother" is probably not acceptable. Not even if I meant it as a joke.

The reason for this small bout of soul-searching is a new book by Melissa Benn (daughter of Labour politician, Tony). What Should We Tell Our Daughters? is Benn's attempt to look at the place of women - she has, like me, two teenage daughters - as we go on into the 21st century. What are their prospects? What problems will they face? How will they fare when it comes to entering the workplace, relationships, the community? How do they negotiate their sexuality, their ambitions ... and can you help them bolster their sense of self?

"I'm a passionate middle-aged feminist," Benn tells me, "but I'm also a typically anxious, concerned mother of teenage girls in the modern world. And I was really interested in what's ahead of them."

This is not an advice book. Rather, Benn hopes, it's the basis of an inter-generational conversation. The cover blurb promises, among other things, "a manifesto for every mother who has ever had to comfort a daughter who doesn't feel pretty". And inevitably, it starts from the author's position as a mother, so the father's role, while not ignored, is slightly secondary. All the more reason to raise it with her, then.

But here's my problem. Benn has spent some time thinking and researching the topic. Most of us haven't put in the work. The thing about parenting is, when you're in the trenches, too often you don't have time to lift your head to see the sky. There's always another parents' meeting/children's party/Pixar movie to go to. As a result, parenting becomes an instinctive thing. And there's a danger in that. Because instinct is another word for doing what your parents did. And our parents aren't necessarily a good model for 21st-century life.

In the 1970s, my dad went to work (when there was work, which wasn't always the case), came home to a cooked dinner, had his clothes washed (though he'd do the ironing from time to time), and put his money on the table. In part that was because he was working full-time as a bricklayer and Mum, a cleaner, was only part-time. It was a reflection of their work patterns. But let's be honest, it was also a reflection of the time. And in that sense you can see a faint link between a brickie who raised his kids in a council house in Northern Ireland and, say, a Labour cabinet minister and political firebrand who raised his family in a four-storey Regency mansion in London's west end.

Melissa Benn grew up watching her father go out to work and speak and be in the world. Tony Benn made a noise. However, it was only when Benn and her brothers grew up that her mother, Caroline de Camp, the eldest child of a well-off Cincinnati family, was able to make her mark as a scholar and campaigner. "My father was of his generation," Benn says. "He was out and about. But I would be the first to say that you want to feel loved, supported, nurtured and he gave all those things." I could say the same of my father. "However," she adds, "in terms of being there in a daily sense, that wasn't what his generation did." And as it was for cabinet ministers, so it was for brickies.

And so, no, Tony Benn didn't do much housework. When she was younger, Benn once made up a series of crude posters showing women hoovering and cooking. "Beneath these," she recalls, "I wrote some deliberately inflammatory slogans about fair sharing of household jobs." Her father, she writes in her new book, loved the argument, and even did a little more in the house for a short time (while also pointing out that the posters' creator was a little lax on the domestic duties front, too).

My generation tends - tends, a nicely slippery word - to be more hands-on. I will wash and iron clothes, vacuum and tidy. I cook too, but usually only at weekends (if we haven't gone for the pizza-and-chips option) and my daily duties pretty much revolve around washing the dishes. Or rather, loading and unloading the dishwasher.

I might have the excuse that I work further away from home than my wife and so in terms of mere utility it's easier if she cooks. There is also, as Benn concedes, an element of women's gatekeeping with their partners - "Oh I'll do it, it's easier" - but maybe we're not too far from the subject of male laziness here.

"You think of it [domestic duty-sharing] in terms of your partner," Benn suggests, "but I wonder if you've ever thought of it in terms of your daughters? I wonder what you will think when your beloved daughters get a degree and then you see them doing endless loads of washing for some guy - you might see it differently."

This is a debate that inevitably starts in the home. As fathers, our domestic relationship with the women in our lives is the first model of masculinity our daughters will have. You could, I suppose, pretend to be Darwinian and argue that your male sense of entitlement is preparing them for the male-dominated world they will grow up into, but that would just be perverse. The challenge is to encourage them to find their own feet when to some degree the odds might be stacked against them.

Is that an out-of-date notion these days? The popular narrative is a girls-on-top one at school - in Britain, almost 30,000 more women than men leave higher education every year with a qualification - and in work, where women have even made the boardroom. That, though, is an optimistic gloss on the reality where women in boardrooms are still the exceptions rather than the rule. And of those who do many have the advantage of coming from an affluent background. It's different for girls at the bottom of the heap. The majority of working-class girls between 14 and 18, when surveyed by the Equality and Human Rights Commission, said they believed they would fail.

How do we address that lack of self-belief? "When girls are teenagers they develop very good emotional skills and are able to see the world and see nuances between people," suggests Benn. "They have ideas about how the world should be. But I don't think they're encouraged to draw those out. School and parents should encourage girls to say what they think. They should ask them what they think and not just about what happened at school - though pay attention to that - but: 'What do you think of the way your school is organised?', 'What do you think about how our home is organised?' - that's where it gets dangerous - 'What do you think about what's happening in the news?'

"The second thing fathers can do," she adds, "is listen. This is a generalisation but if we're going to change the balance of power in society women have to learn to speak more and perhaps men must learn also to develop that skill to listen.

"It's the opposite of telling, but you're giving her a tremendous gift. Really listen, don't just put on a listening face. I remember this as a young woman. There was nothing I hated more than speaking and feeling that something was not being translated and I was not being paid attention to. And I wasn't being particularly demanding. I wasn't a prima donna. I just knew. I had that sense as a young woman of not having any weight in the world. And I think we've got to give our daughters attention. That's not making them privileged and spoilt but taking them seriously."

Although I have to admit my listening face is really, really convincing, I hope I do listen. I guess only my daughters will know if that helps.

Speaking matters too, though. Because at some level we do need to address the nature of the culture our daughters are growing up into. In a world of social media in which a virulent misogyny is currently at large - ask Mary Beard - there is a widespread sexualisation and even pornification of the culture. Perhaps it's assumed that these are areas where mothers stand up for daughters more readily.

As Benn points out, it was Mumsnet which made an issue of the sexualisation of young girls' clothing. But often it is men's voices that can cut through. Think of the impact of the actor Patrick Stewart's revelation of the physical abuse heaped on his mother by his father in 2009. "I would say to all fathers, you have that weight behind you," says Benn. "Please use it to put your voice behind all these issues."

As a father, then, I am always informing my daughters on the world - for good or ill - in what I say and in how I act. Maybe, too, in how I vote. We are seeing the props of the welfare state - the safety-net that saw both myself and Benn get an education (free back then) and kept us well and helped give us care for our children - being knocked out from under the rising generation. We need to speak up for what we are losing because our daughters (and sons) will suffer if it disappears. "If we don't fight for it," Benn points out, "it's going to really affect our daughters and it's going to divide our daughters. Everybody needs a society that's there to support you at some point."

But support begins with fathers and mothers (if you're lucky to have both). Our daughters (and sons, of course) will face challenges we can't even imagine yet. All we can do as parents is try to give them a foundation of confidence and self-belief to face those challenges head-on.

It doesn't matter who relays the message. Maybe, as Benn suggests, it might be the dad who will tell you how to make a great spag bol and the mum who will tell you how to ask for a pay rise (if such a thing still exists). But as long as we're there for advice and support, that's a start. Until such times as mum and dad are no longer required.

My 17-year-old recently started college. She's meeting new friends, beginning to take some baby steps out into the world. I doubt she'll be moving out any time soon but at some point it will happen. I'm not wishing it but I also know it will be what she needs to do. I suppose that's the last thing a father can usefully tell a daughter. That it's OK to find her own way.