We study the formation of early-type galaxies (ETGs) through mergers with a sample of 70 high-resolution (softening length <60 pc and 12 × 106 particles) numerical simulations of binary mergers of disc galaxies (with 10 per cent of gas) and 16 simulations of ETG remergers. These simulations, designed to accompany observations and models conducted within the ATLAS3D project, encompass various mass ratios (from 1:1 to 6:1), initial conditions and orbital parameters. The progenitor disc galaxies are spiral-like with bulge-to-disc ratios typical of Sb and Sc galaxies and high central baryonic angular momentum. We find that binary mergers of disc galaxies with mass ratios of 3:1 and 6:1 are nearly always classified as fast rotators according to the ATLAS3D criterion (based on the λR parameter – ATLAS3D Paper III): they preserve the structure of the input fast rotating spiral progenitors. They have intrinsic ellipticities larger than 0.5, cover intrinsic λR values between 0.2 and 0.6, within the range of observed fast rotators. The distribution of the observed fastest rotators does in fact coincide with the distribution of our disc progenitors. Major disc mergers (mass ratios of 2:1 and 1:1) lead to both fast and slow rotators. Most of the fast rotators produced in major mergers have intermediate flattening, with ellipticities ε between 0.4 and 0.6. Most slow rotators formed in these binary disc mergers hold a stellar kinematically distinct core (KDC) in their ∼1–3 central kiloparsec: these KDCs are built from the stellar components of the progenitors. However, these remnants are still very flat with ε often larger than 0.45 and sometimes as high as 0.65. Besides a handful of specific observed systems – the counter-rotating discs (2σ galaxies, ATLAS3D Paper II) – these therefore cannot reproduce the observed population of slow rotators in the nearby Universe. This sample of simulations supports the notion of slow and fast rotators: these two families of ETGs present distinct characteristics in term of their angular momentum content (at all radii) and intrinsic properties – the slow rotators are not simply velocity-scaled down versions of fast rotators. The mass ratio of the progenitors is a fundamental parameter for the formation of slow rotators in these binary mergers, but it also requires a retrograde spin for the earlier-type (Sb) progenitor galaxy with respect to the orbital angular momentum. We also study remergers of these merger remnants: these produce relatively round fast rotators or systems near the threshold for slow rotators. In such cases, the orbital angular momentum dominates the central region, and these systems no longer exhibit a KDC, as KDCs are destroyed during the remergers and do not re-form in these relatively dry events.