Intelligence in large-brained vertebrates might have evolved through independent, yet similar processes based on comparable socioecological pressures and slow life histories. This convergent evolutionary route, however, cannot explain why cephalopods developed large brains and flexible behavioural repertoires: cephalopods have fast life histories and live in simple social environments. Here, we suggest that the loss of the external shell in cephalopods (i) caused a dramatic increase in predatory pressure, which in turn prevented the emergence of slow life histories, and (ii) allowed the exploitation of novel challenging niches, thus favouring the emergence of intelligence. By highlighting convergent and divergent aspects between cephalopods and large-brained vertebrates we illustrate how the evolution of intelligence might not be constrained to a single evolutionary route.