It's not entirely ahistorical, but it's value-laden. The period of in between 1959 and 1963 saw a change in the music that was popular amongst young people in Anglophone countries, where the rock'n'roll style of the 1955-1958 period was replaced in prominence by a more melodic Brill Building-based sound, based around a teen-oriented variation on Tin Pan Alley songwriting. 1960 is sometimes considered the nadir; to quote from Bob Stanley's book Yeah Yeah Yeah:

1960 was a hiatus in modern pop. To kids who had grown up with the shrill call to arms of ‘Good Golly Miss Molly’ or ‘Rave On’, turning on the radio and hearing the lightweight pleasures of Frankie Avalon’s ‘Why’ (US no. 1 ’60), or Cliff Richard’s ‘Voice in the Wilderness’ (UK no. 2 ’60), it might have seemed the moment to move on to different interests: American students like Minnesota’s Robert Zimmerman had their intellect tickled by folk; in Britain, mods and beatniks eschewed pop for various kinds of jazz.

As to what was replacing 'Good Golly Miss Molly' or 'Rave On' in this era, it was most often 'teen idols' and 'girl groups'. Think, for example, the very successful songwriting team of Gerry Goffin and Carole King, who wrote and produced songs destined to be sung by relatively anonymous singers or groups (e.g., Little Eva, who did 'The Loco-Motion' or Maxine Brown who did the original 'Oh No Not My Baby').

To quote again from Stanley's Yeah Yeah Yeah:

Connie Francis and Brenda Lee had made records that wouldn’t scare your parents; the girl groups of the early sixties didn’t even consider what adults might think. They made records about and for a complete teenage world. The Shirelles from Passaic, New Jersey, were first on the scene in late 1960 with Goffin and King’s first hit, ‘Will You Love Me Tomorrow’ (US no. 1, UK no. 3)... The bravery of ‘Will You Love Me Tomorrow’, with its post-virginal lyric, was something new, and the Shirelles were soon followed by interchangeable acts of girls who had met in high school and were often pictured in their prom dresses. Often, they were looking not for a long-term music career, or a way of making it to Hollywood, but simply for something fun to do for a couple of years before they got married and had kids. This gave their singing and their records a sense of spontaneity and freshness: ‘Goodbye Cruel World’ may not get much airplay these days, but the Crystals’ ‘Then He Kissed Me’ certainly does....As the Beatles dominated the British charts in 1963, the girl-group sound peaked in the States: fifty-one per cent of the year’s Top 20 hits were made up of female-vocal or mixed-vocal records, the majority of which were Brill Building songs...

Which is to say that part of why the Brill Building stuff was seen as lesser was that the music was gendered, and its appeal at the time was more about people exploring ideas of femininity rather than exploring ideas of masculinity (and so, perhaps unsurprisingly was not as appreciated by the teenage boys of the era who later wrote the popular narrative of rock'n'roll).

As to whether the rock'n'roll of 1956 is 'better' than 'Will You Love Me Tomorrow', well, that's based on what you value in music and the relative importance you place on different parts of music. The music of 1956 was full of an energy and excitement that wasn't always present in the Brill Building sound, but there's a songcraft in the Brill Building stuff, and a melodicism which wasn't as prominent in the rock'n'roll of 1956; a lot of what the resurgence of guitar-based rock'n'roll in 1963/1964 did was to take the energy and excitement of 1950s rock'n'roll and ally it to the songwriting craft and skill of the Brill Building stuff; it's not for nothing that the Lennon & McCartney stated that they wanted to be the next Goffin & King, or that British Invasion groups like Herman's Hermits commonly covered songs like Goffin & King's 'I'm Into Something Good').

As to why the change in sounds happened, partly it's simply music styles inevitably going in and out of fashion - after a few years, people usually want other sounds. But also, another reason (as discussed extensively in The Sound Of The City by Charlie Gillett) is the way that the major record labels and minor record labels worked in the era. The bigger recording companies (the major labels) had significantly more resources and connections than smaller recording companies (the minor labels) in a way that meant that they had the capability to dominate the market with the right product. But with that size came a level of bureaucracy, concern about demographics, concern about signing long-term prospects that wouldn't go out of fashion with the next fad, and a certain desire amongst management for respectability.

All of this, ultimately, led to a certain lack of understanding of the appeal of 1950s rock'n'roll. Additionally, pop music aimed at teenagers was, as far as they were concerned, often only one niche amongst many in their catalogues - while it's certainly prominent now because those teenagers grew up and continued liking the music, it wasn't necessarily the majority of their sales (especially of albums, which typically seemed to be bought by more adult audiences, and where the profit margin was better). All of this meant that the major record labels were relatively slow to respond to 1950s rock'n'roll, and when they did, they typically were a little uncomfortable with the roughness of the music, feeling that it would do better commercially with the edges sanded off. As the major record labels understood it, teen idols like Elvis would need to move towards the centre with their career, basically becoming plausible light entertainment personalities - e.g., the Frank Sinatras of the next generation (as Sinatra himself had once been a teen sensation with teenage fans), who appealed across generations (e.g., might actually appeal to the older people within the record companies making the decisions).

That said, if you were following music on minor labels seen as rhythm & blues specialty labels (as the Beatles obviously were), there was still plenty of interesting music occuring in the 1959-1963. This is the era when minor labels focused on rhythm & blues music, like Motown, Stax, and Vee Jay came to prominence, often making music with a roughness and energy missing from the major label pop music of the era. The Isley Brothers' 'Shout' was 1959. 'Money' by Barrett Strong (and written by Berry Gordy, and basically the first song on the Motown record label) came out in 1959, and Motown went from strength to strength, with early successes from the likes of the Miracles and Marvin Gaye (and despite their later reputation for smooth sophistication, the early years of Motown definitely had rough edges and excitement - Little Stevie Wonder's first big hit 'Fingertips' in early 1963 was all about energy and excitement in a way that would have appealed to fans of 1950s rock'n'roll. Otis Redding's 'These Arms Of Mine', his breakout hit, was released in October 1962, the month after Booker T & The MG's 'Green Onions'. Similarly, in a more blues sense, Chess Records continued to release what turned out to later be influential recordings during the 'rock'n'roll is dead' period, such as Howlin' Wolf's versions of 'Spoonful' (1960), 'Red Rooster' (1961), and 'I Ain't Superstitious' (1962), or Muddy Waters' version of 'Got My Mojo Working' (1960) and 'You Need Love' (1962).

Additionally, in terms of rock'n'roll made by white people between 1959-1962 that had the roughness and energy of the 1950s rock'n'roll, you're probably looking at the instrumental guitar groups; think The Ventures' 'Walk Don't Run' (1960), The Fireballs' 'Bulldog' (1960), Dick Dale and the Del-Tones' 'Misirlou' (1962), and The Tornadoes' 'Telstar' (1962). But there's still vocal rock'n'roll of the era that doesn't exactly fit into the teen pop Brill Building thing; most prominently, Roy Orbison's mini-operas like 'Runnin' Scared' (1962) and 'It's Over' (1962), but also Del Shannon songs like 'Runaway' (1961) and Dion's 'The Wanderer' (1961).

But basically, when it comes down to it, the usual story of rock'n'roll was written by white male baby boomers, and what happened in pop music in 1963/1964 reflected their beliefs about the world in a way that the teen Brill Building pop of the late 1950s-early 1960s did not; as later generations came to see the history of rock in different ways, with different beliefs about what to value in music (e.g., punks like Blondie and the Ramones who were suspicious of hippies and 1960s authenticity), the Brill Building stuff was re-evaluated and things like 'Will You Still Love Me Tomorrow' came to be more likely to end up in 'top 100 best 1960s songs of all time' lists.

As to signposts in the early 1960s towards what came next: well, pretty much everything above! By 1965 or so, rock wasn't really the same music as rock'n'roll had been in 1956. In addition to something of the sound and energy of 1950s rock'n'roll, it had the countercultural concerns of early 1960s folk, the emphasis of songcraft of the Brill Building/girl group stuff, an approach to masculinity, and an attitude most indicative of Chicago blues (e.g., Chess Records), and something of the dance beats and gospel influenced vocals of 1960s soul. The focus on the guitar in 1960s rock wasn't so present in 1950s rock'n'roll, and comes a bit from the instrumental guitar groups, a bit from the Chicago blues and, a bit from of the adventurousness and focus on instrumental virtuosity of post-bop jazz (and in particular jazz guitarists like Charlie Byrd who likely influenced the name of the rock band The Byrds).