It is a strange and beguiling experience to find music you have had in your head since childhood reveal new and unsuspected shades of meaning 50 years later. Beatles songs aren’t like most pop songs; instead of fading, they take on a richer colour and nuance, not least because new generations of fans inquire more deeply into what previous listeners might have overlooked or simply misunderstood. One twist of the kaleidoscope and a song we thought we knew suddenly sounds even better than it did the first 100 times we heard it.

This is the effect of reading Ian Leslie’s brilliant study of the Beatles’ music, a book that offers not only a lesson in listening (again) but an enthralling narrative of friendship, creative genius and loss. At its centre is the songwriting partnership of John Lennon and Paul McCartney, and the unprecedented peaks the two of them scaled in remaking English popular music. You may find it impossible not to be awed by their achievement all over again. But Leslie also wants to challenge a myth about the pair. After the Beatles finally disbanded, a consensus formed that Paul was the straight man to John’s rebel bohemian – vanilla against brimstone – which hardened into holy writ on Lennon’s murder in 1980. McCartney’s inadequate off-the-cuff response to the news (“it’s a drag”) took some living down. Leslie lays to rest this old opposition, arguing that there was “no John without Paul, and vice versa”. Their collaboration was as tight and co-dependent as two climbers roped together on a mountain face.

The two boys who met in 1957 at a summer fete in Woolton village were bonded by talent and by family tragedy. Both had lost their mothers when they were teenagers, a spiritual wound that was borne in silence but linked them in understanding. “In music they could say what they felt without having to say it.” As they practised at home, they taught each other the art of songwriting and intuitively felt their way into a partnership. Leslie conveys the excitement and pace of this self-discovery, from the fledgling years of Hamburg and the Cavern through the “ecstatic bounce” of Please Please Me to the end of 1963, when they had four No 1 singles and two No 1 albums.

He is also alert to the way their songs reverberate between eras. The first song McCartney ever wrote, I Lost My Little Girl, just after the death of his mother, is captured again when the band play it together during the Get Back sessions at Savile Row in January 1969. He spots another proleptic link from the unusual dynamic dramatised in She Loves You, “a boy-girl love song about friendship between boys”: 11 years later, McCartney was a real-life go-between for Lennon during a crisis with Yoko Ono.

But Leslie scores highest in his penetrating analysis of the differences that drove their creative alchemy. As the songwriting grew in complexity, their characters emerged more distinctively: Lennon being sardonic, self-critical, volatile; McCartney romantic, joyous and inquisitive. In time, a rivalry flared up, and yet far from stalling the partnership, it inspired them to greater heights of inventiveness and daring. Two pairs of songs, close upon one another, illustrate this duelling spirit. In early 1966 Lennon wrote Tomorrow Never Knows after hearing McCartney play Eleanor Rigby, disparate in mood and effect yet both built on an alternation between two chords. Leslie’s musical ear picks up the odd consonances between the pair and “the sounds of words as connecting fibres”, the mirroring of phrases and gaze-of-eternity perspective. Counterintuitively, the Lennon song is emollient in its message, the McCartney cheerless and unforgiving, yet “the two songs speak to one another”.

In another great cadenza, Leslie considers the double vision of the single Penny Lane and Strawberry Fields Forever, obverse sides of the same golden coin; this time Lennon’s fugue-like journey into the unconscious set against McCartney’s jaunty “toytown diorama” with its everyday characters made strange – “McCartney’s Magritte”, as Leslie calls it. Of all the songs featured here, these are the two that flame brightest in the author’s close interpretation, and I felt I was understanding them properly for the first time. In Penny Lane we hear “the singer-narrator has a child’s enthusiasm and an adult’s experience”; in Strawberry Fields Forever we hear anew its “gauzy ambiguity” between dream and nightmare: “The listener is oriented just enough to take pleasure in being lost.”

This takes us into 1967, “the year when John and Paul were most in sync”, to the point where their actual voices were sometimes hard to tell apart. They even dreamed the same dreams. But their different personalities were becoming marked, partly under the influence of drugs, partly through Lennon’s increasing fragility and neediness. “Only when he was working with Paul did he feel like a genius.” Leslie has previously written books on human psychology, and here he gets thoroughly stuck into the crosscurrents of dependence and resentment that roiled beneath the surface.

At times, he sounds like a couples therapist, and indeed when Ono enters the scene, he identifies Lennon’s new alliance as a “triangulation”, the possibly unconscious undermining of a partner through befriending a third party. Woah, heavy!, you think, and yet it might make perfect sense. It doesn’t require a psychologist, of course, to hear deep strains of depression and paranoia in a lament such as Yer Blues, but Leslie’s occasional overegging of the psychodrama tips the mood towards daytime soap: “John thought Paul understood how insecure he felt… and sought emotional reassurance. Paul thought John needed to feel he was the most important person in the group: hence his insistence that John is the boss. But John didn’t want power, not any more. He wanted love.”

The book’s subtitle is nonetheless pertinent, since it really is a love story, and in Lennon’s mind might have been something more. During the Get Back sessions, he says to McCartney, only half-joking: “It’s like you and me are lovers.” When their partnership was sundered at last, the fallout was commensurately intense, with Lennon vituperating McCartney as bitterly as any scorned ex. His rancorous denunciation of McCartney in How Do You Sleep? on the Imagine album shocked at the time, but now sounds “preposterous” (“The only thing you done was Yesterday”), as did a lot of the interviews he gave in the aftermath of the split. The relationship eventually recovered, albeit hedged around by Lennon’s enthralment to Ono. What came as a surprise to me – one of several here – was the story of Lennon being galvanised to make music again on hearing McCartney’s Coming Up on the radio (“It’s driving me crackers”).

I had up to now considered the gold standard of Beatles books to be Ian MacDonald’s formative Revolution in the Head, published more than 30 years ago. John & Paul is its equal in passionate engagement with the songs and possibly its superior in originality. But is it too late to register a regret that one vital song has been overlooked? And Your Bird Can Sing is a sour-sweet blast of energy that perfectly fits Leslie’s argument about the two writers talking to each other, a song of misunderstanding that both airs a grievance (“You can’t hear me”) and offers reconciliation (“Look in my direction, I’ll be round”). There’s an outtake of the song on The Beatles Anthology when McCartney starts giggling, which sets off Lennon, and they both laugh helplessly through to the end. It reminds you what fun, aside from everything else, genius could be.

The Mouthless Dead by Anthony Quinn is published by Abacus (£20)

• John & Paul: A Love Story in Songs by Ian Leslie is published by Faber (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply