We propose a simple model for the origin of fast and slow rotator early-type galaxies (ETG) within the hierarchical Λcold dark matter (ΛCDM) scenario, that is based on the assumption that the mass fraction of stellar discs in ETGs is a proxy for the specific angular momentum expressed via λR. Within our model we reproduce the fraction of fast and slow rotators as a function of magnitude in the ATLAS3D survey, assuming that fast-rotating ETGs have at least 10 per cent of their total stellar mass in a disc component. In agreement with ATLAS3D observations we find that slow rotators are predominantly galaxies with M* > 1010.5M⊙ contributing ~20 per cent to the overall ETG population. We show in detail that the growth histories of fast and slow rotators are different, supporting the classification of ETGs into these two categories. Slow rotators accrete between ~50 and 90 per cent of their stellar mass from satellites and their most massive progenitors have on average up to three major mergers during their evolution. Fast rotators in contrast accrete less than 50 per cent and have on average less than one major merger in their past. We find that the underlying physical reason for the different growth histories is the slowing down and ultimately complete shut-down of gas cooling in massive galaxies. Once cooling and associated star formation in disc stop, galaxies grow via infall from satellites. Frequent minor mergers thereby destroy existing stellar discs via violent relaxation and also tend to lower the specific angular momentum of the main stellar body, lowering λR into the slow rotator regime. On average, the last gas-rich major merger interaction in slow rotators happens at z > 1.5, followed by a series of minor mergers. These results support the idea that kinematically decoupled cores (KDC) form during gas-rich major mergers at high z followed by minor mergers, which build-up the outer layers of the remnant, and make remnants that are initially too flat compared to observations become rounder. Fast rotators are less likely to form such KDCs due to the fact that they have on average less than one major merger in their past. Fast rotators in our model have different formation paths. The majority, 78 per cent, has bulge-to-total stellar mass ratios (B/T) > 0.5 and managed to grow stellar discs due to continued gas cooling or bulges due to frequent minor mergers. The remaining 22 per cent live in high-density environments and consist of low B/T galaxies with gas fractions below 15 per cent, that have exhausted their cold gas reservoir and have no hot halo from which gas can cool. These fast rotators most likely resemble the flattened disc-like fast rotators in the ATLAS3D survey. Our results predict that ETGs can change their state from fast to slow rotator and vice versa, while the former is taking place predominantly at low z (z < 2), the latter is occurring during cosmic epochs when cooling times are short and galaxies gas-rich. We predict that the ratio of the number density of slow to fast rotators is a strong function of redshift, with massive (>1010M⊙) fast rotators being more than one order of magnitude more frequent at z~ 2.