Malala Yousafzai says she's lost herself. "In Swat [district], I studied in the same school for 10 years and there I was just considered to be Malala. Here I'm famous, here people think of me as the girl who was shot by the Taliban. The real Malala is gone somewhere, and I can't find her."

We are sitting in a boardroom on the seventh floor of the new Birmingham library, the glass walls allowing us a view of a city draped in mist, a sharp contrast to the "paradise" of Swat, with its tall mountains and clear rivers which Malala recalls wistfully. It should be desperately sad but the world's most famous 16-year-old makes it difficult for you to feel sorry for her. In part, it is because she is so poised, in a way that suggests an enviable self-assurance rather than an overconstructed persona. But more than that, it is to do with how much of her conversation is punctuated by laughter.

The laughter takes many forms: self-deprecating when I ask her why she thinks the Taliban feel threatened by her; delighted when she talks of Skyping her best friend, Muniba, to get the latest gossip from her old school; wry when she recalls a Taliban commander's advice that she return to Pakistan and enter a madrassa; giggly when she talks about her favourite cricketers ("Shahid Afridi, of course, and I also like Shane Watson"). And it's at its most full-throated when she is teasing her father, who is present for part of our interview. It happens during a conversation about her mother: "She loves my father," Malala says. Then, lowering her voice, she adds: "They had a love marriage." Her father, involved in making tea for Malala and me, looks up. "Hmmm? Are you sure?" he says, mock-stern. "Learn from your parents!" Malala says to me, and bursts into laughter.

Learning from her parents is something Malala knows a great deal about. Her mother was never formally educated and an awareness of the constraints this placed on her life have made her a great supporter of Malala and her father in their campaign against the Taliban's attempts to stop female education. One of the more moving details in I Am Malala, the memoir Malala has written with the journalist Christina Lamb, is that her mother was due to start learning to read and write on the day Malala was shot – 9 October 2012. When I suggest that Malala's campaign for female education may have played a role in encouraging her mother, she says: "That might be." But she is much happier giving credit to her mother's determined character, and the example provided by her father, Ziauddin, who long ago set up a school where girls could study as well as boys, in a part of the world where the gender gap in education is vast.

The 15-year-old pictured at Queen Elizabeth hospital in Birmingham, to which she had been rushed for an operation. Photograph: University Hospitals Birmingham/PA

It is hard to refrain from asking Ziauddin Yousafzai the "do you wish you hadn't …?" question about his daughter, whose passion for reform clearly owes a lot to the desire to emulate her education-activist father. But it's a cruel question, and unfair, too, given my own inability to work out what constitutes responsible parenting in a world where girls are told that the safest way to live is to stay away from school, and preferably disappear entirely.

It is perhaps because of criticism levelled at her father that Malala mentions more than once in her book that no one believed the Taliban would target a schoolgirl, even if that schoolgirl had been speaking and writing against the Taliban's ban on female education since the age of 12. If any member of the family was believed to be in danger, it was Ziauddin Yousafzai, as much a part of the campaign as his daughter. And it was the daughter who urged the father to keep on when he suggested they both "go into hibernation" after receiving particularly worrisome threats. The most interesting detail to emerge about Ziauddin from his daughter's book is his own early flirtation with militancy. He was only 12 years old when Sufi Mohammad, who would later be a leading figure among the extremists in Swat, came to his village to recruit young boys to join the jihad against the Soviets in Afghanistan. Although Ziauddin was too young to fight then, within a few years he was preparing to become a jihadi, and praying for martyrdom. He later came to recognise what he experienced as brainwashing – and was saved from it by his questioning mind and the influence of his future brother-in-law, a secular nationalist.

The information about her father's semi-brainwashing forms an interesting backdrop to Malala's comments when I ask if she ever wonders about the man who tried to kill her on her way back from school that day in October last year, and why his hands were shaking as he held the gun – a detail she has picked up from the girls in the school bus with her at the time; she herself has no memory of the shooting. There is no trace of rancour in her voice when she says: "He was young, in his 20s … he was quite young, we may call him a boy. And it's hard to have a gun and kill people. Maybe that's why his hand was shaking. Maybe he didn't know if he could do it. But people are brainwashed. That's why they do things like suicide attacks and killing people. I can't imagine it – that boy who shot me, I can't imagine hurting him even with a needle. I believe in peace. I believe in mercy."

Well, I believe in these things, too, but if someone put a bullet in my head I suspect I would be more than a little irate. Doesn't she feel at all angry? "I only get angry at my brothers, and at my father," she says. Particularly her brother Khushal, who is two years younger than her. "I can't be good to him, it's impossible. We can't ever be friends," she says, sounding like the teenager she is.

Schoolgirls in New Delhi wear Malala masks as part of a campaign to win greater resources for education in India. Photograph: Altaf Qadri/AP

Perhaps meditating on the value of peace and mercy is an entirely sane way of coping with bullets and invective. But, all the same, it must hurt to find yourself reviled – and not only by the Taliban. In her book she writes of how her speech at the UN received plaudits around the world, but in Pakistan people accused her of seeking fame and the luxury of a life abroad. When I ask her about this, it is one of the only times in the conversation that she turns to Urdu to express herself: "Dukh to insaan ko hota hai jab daikhta hai kay uss ka bhai uss kay khilaf hai." ("Naturally it's hurtful when you see your brothers turn against you.") Her voice is pained, but she quickly switches to English and the more philosophical tone emerges again. "Pakistanis can't trust," she says. "They've seen in history that people, particularly politicians, are corrupt. And they're misguided by people in the name of Islam. They're told: 'Malala is not a Muslim, she's not in purdah, she's working for America.' They say maybe she's with the CIA or ISI [Pakistan's intelligence service]. It's fine; they say it about every politician too, and I want to become a politician."

That line is a joke, insofar as she sees the humour in it; but it is nonetheless a statement of intent. She really does believe she will go back to Pakistan – "inshallah, soon" – and replies like a seasoned politician when I ask which political party she'll join. "I haven't chosen any party yet because people choose parties when they get older. When it's time I'll look and if I can't find one to join, I'll make another party."

She is, at first, similarly noncommittal about what she thinks of conversations around the burqa in the UK. "I don't have a specific idea about that," she says. But quickly, it's clear she does. "I believe it's a woman's right to decide what she wants to wear and if a woman can go to the beach and wear nothing, then why can't she also wear everything?" Having said that, she doesn't think a woman should cover her face in court or in other places "where it's necessary to show your identity. I don't cover my face because I want to show my identity."

Malala Yousafzai: her laughter takes many forms, from self-deprecating about why the Taliban feel threatened by her to giggly when talking about cricketers. Photograph: Christopher Thomond for the Guardian

This desire to be visible meant she wasn't at all happy, aged 12, when the BBC insisted that she use a pen name to write her diary of a schoolgirl living under the Taliban. "I still think, why didn't I write as Malala? But the BBC was doing it for my security. They didn't want me to be killed for" – and here she laughs – "writing a diary for BBC Urdu. So, if you look at it in another way, they were really kind because they were thinking about my life." She clearly believes the decision was as misguided as it was well-intentioned. You can't campaign invisibly.

I try to draw her on the question of how she finds life in the UK, and what an average day is like. There is clearly something of culture shock – quite other than the fact that the girls in school don't see "the real Malala". She says the environment here is different to everything she knew before – the way the girls interact, their manner of gossip and play, are all unfamiliar. And everyone takes education for granted; school isn't the "Aladdin's lamp … the doorway to a magical world" as it was for the girls in Swat. For the moment, it seems her main concern is how many A grades she will get in her GCSEs next year, but "the hard thing is now my life is very busy and I have so many responsibilities and duties that I need to fulfil."

Unlikely as a 16-year-old with a burning passion for reform and education might be, there is no doubt she is entirely genuine. In fact, the points at which I found myself raising an eyebrow at her book had nothing to do with extraordinary maturity or resolve but, rather, references to Justin Bieber and Twilight which seem forced in by someone trying to point out that in some ways she is "a normal teenager". When I bring up pop culture, it's the only time she appears to be on the back foot. She struggles to tell me names of Pakistani singers she likes, and finally comes up with "the woman who sang Ek Bar Muskara Do" (Smile Just Once) – the name she is looking for is Munni Begum, a classical singer who did a well-known cover of that 1972 song, years before Malala was born. When I tell her the question isn't important she says that she does like some English-language songs, but "most of them I can't understand. They say words and words and words, and I don't know what they're telling me. I like songs with a meaning."

It isn't that she doesn't have any interests beyond her education campaign; it's just that "a normal teenager" in Swat isn't defined by Justin Bieber and Twilight. If you really want to get her animated, talk about the one subject that can make almost any Pakistani turn into a bit of a teenager: cricket. She follows it closely on TV (which isn't unusual for girls in Pakistan), and also plays (which is). When she sees that I am interested in talking to her about the game everything in her poised manner changes. Within seconds she's calling out "Howzat!" and "Siiiiiix!" and showing me the deficiencies of her bowling action (she's a wrist spinner, though she prefers to bat). When I mention the Birmingham women's cricket club she says: "Yeah, I would like to join them."

Speaking in Dublin in September after receiving the Amnesty International ambassador of conscience award. Photograph: Aidan Crawley/EPA

She is so entirely sparkling and alive, with no sign of the Taliban or education or responsibilities intruding on her memories of playing cricket on the rooftop of her house with the mountains as backdrop, that I wish I could take her to Lord's instead of plying her with questions. Does it get lonely, knowing there is no one else in the world who has had the same experience as her? I don't just mean being shot by the Taliban, which is a tragically common experience, but the attention that followed. It's the only time she doesn't understand what I am asking her. I explain and she says: "When someone tells me about Malala, the girl who was shot by the Taliban – that's my definition for her – I don't think she's me. Now I don't even feel as if I was shot. Even my life in Swat feels like a part of history or a movie I watched. Things change. God has given us a brain and a heart which tell us how to live."

The interview ends soon after and the photographer is in the middle of taking pictures when the door opens and her father, who had left halfway through the interview, walks in with a group made up mostly of men. At their head is Chaudhry Abdul Majeed, the prime minister of Azad Jammu and Kashmir. Photographs are taken, everyone sits down, and the prime minister starts talking – about what I already can't remember. He is still talking when I leave the room, and still talking when I turn around for my last glimpse of Malala: she is sitting silently, stoically, being talked at. The girl who shouted "Howzat!" has disappeared and in her place is Malala, the girl who was shot by the Taliban.

I Am Malala: The Girl Who Stood Up For Education and Was Shot By The Taliban by Malala Yousafzai and Christina Lamb, is published by Wiedenfeld & Nicolson at £18.99.