Autobiography tells the whole story of a life. It leaves nothing, or little, out. This is because autobiography is the province of famous people. The writer of autobiography – that is, the famous person – doesn’t need to work to gain the reader’s attention; that attention already exists. Therefore, all events are of interest. Memoir, on the other hand, must earn the reader’s attention, because the writer of memoir – that is, a person hitherto unknown to their audience – recognises her story is not of inherent importance. The way memoir makes a story is by leaving things out. It’s hard, disciplined work. Life feels infinite to each of us, like a massive eternally unfurling bolt of fabric – fabric that must be cut to make a story. This cutting is how a memoirist takes care of her reader. Structure in the memoir, then, has to do with what is omitted.

Rose Boyt’s new book ranges across her life in a story that is shaped – very loosely– by three experiences of sitting for her father, the painter Lucian Freud. The first sitting occurs when she’s 18 and posing for the portrait that gives this book its title. The painting shows the author, naked, sprawled in an attitude of abandon, her legs spread and a blanket twined around her feet as though she is recovering from sexual athletics. Boyt writes: “My father didn’t want to work from me again after the completion of the naked portrait. I think he had done all he could – the painting said everything …” There is, indeed, a terrifying completeness to the work; Freud’s daughter has been represented to the utmost.

The second portrait session happens in 1990, when Boyt has developed a confrontational relationship with her father. She is clothed here, but the painting still has a profound vulnerability to it. The third painting is a group portrait of Boyt, her husband, his child, their baby and another baby in utero. Here, she seems safe, buttressed by the people around her.

I confess I hoped that Boyt would focus on the naked portrait of the title. I was interested to read a book exploring the strange power dynamic that develops when one person is naked and the other clothed. (Perhaps this is of special interest to me because I worked as a nude model myself in my younger, broker days.) I wanted the painter-subject relationship anatomised and I wanted it complicated by the father-daughter story. But Boyt quickly moves past her earliest sitting for her father to tell, in looping anti-chronology, of the poverty and chaos of her childhood, of her father’s rare appearances in her life, of the difficulty and wildness of her coming of age, and of her mother Suzy Boyt’s impulsive pursuit of her own relationships, often to the detriment of the children’s safety.

Particularly harrowing is her account of the period her family spent living on a cargo ship with her mother’s predatory boyfriend, who seems to have taken every opportunity to ogle and paw little Rose. (Also, the boat sank.) Her life story throughout involves the breaching of boundaries. We learn of her father’s sex talk with her from a very young age and of his sexual relationships with her friends; of handsy acquaintances of her parents; and of her rape at the age of 14 by one of her brother’s friends. After her mother dies, “I remembered in my fresh grief a conversation I had had with Ali [her brother] many years after the rape, when I tried to make him understand what his friend had done and he made the same type of mildly uneasy response as my father, just sort of shit happens”. Naked Portrait can be seen as Boyt’s attempt to push past “shit happens” and unearth the truth of her life.

In certain ways she succeeds: the unexpected miracle of the book is its emotional complexity. Writing about her father, Boyt teeters like Buster Keaton: “of course he loved me, he bought me a flat, he never told me he loved me, maybe he didn’t love me, of course he loved me.” Such ambivalence marks any human relationship; the chaos of Boyt’s family life certainly must have created a kind of training ground for warring emotions.

Any person who has lived through a tumultuous and lie-festooned childhood will be on the lookout for an aide-memoire – something to shore up the crumbling banks of memory. As she sets out to write her life story, Boyt discovers her journal: “clearing out of our house to make way for builders, I found an old diary in a cardboard box, hundreds of typed pages …” A large portion of the book involves her quoting at length from the diary and then breaking in to clarify and expand on what she has found. You can feel the energy of her discovery of the younger self.

Some of the material in her back pages is worthy of our rubbernecking: she meets Andy Warhol and he farcically proposes to her; she hangs out with her pal Neneh Cherry; she rubs shoulders with her father’s artist friends. But the book suffers from an absolute avalanche of detail about her experiences as a bohemian young woman in 1970s and 80s London. I’m a bit younger than Boyt and have long harboured a fascination with this milieu, but even I got swamped.

Boyt has made an error: she has mistaken her interest in her younger self for our interest in her younger self, and has failed to cut and prune and generally manage her material according to any concern for the reader’s experience. I wonder if this error has to do with the strange almost-public nature of her story. She’s not famous, but her father is. She’s not famous, but her siblings are. This approximate fame has led her to write a book that is too much autobiography and not enough memoir – a book that refuses to do the hard work of omission.

Of course it’s the portrait of Lucian that will bring attention to her story – and a very naked portrait it is. Recently, Boyt gave an interview in which she said she didn’t write her book in order “to cancel him or whatever”. But what is cancelling? It’s simply saying what happened. She is making this claim about not wanting to cancel him after she has already performed, in the book, the speech-act that constitutes “cancellation”. This after-the-fact attempt to erase her own speech could be seen as revealing her uncertainty about what is public and what is private. Is she simply saying what happened to her, as a private person, or is she levelling a charge against a public figure? Naked Portrait can be read as a book by a person unresolved about her own status.

At the same time, this lack of understanding could be thought of as a very common contemporary malaise. We live in a moment when we know everything about everyone. We become confused about our level of known-ness. Naked Portrait reads strangely as a kind of Pilgrim’s Progress of the biographical era, when our heroine has no true understanding of her role in the public imagination. And nor do any of us. If we’re all famous, we all deserve to turn our backs on the labour of memoir and instead write autobiographies. The thought makes me exhausted.

• Claire Dederer is the author of Monsters: What Do We Do With Great Art by Bad People? (Sceptre). Naked Portrait by Rose Boyt is published by Picador (£18.99). To support the Guardian and the Observer order your copy at guardianbookshop.com. Delivery charges may apply.