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We study the origin of the wide distribution of angles between the angularmomenta of the stellar and gas components, $\alpha_{\rm G,S}$, in early-typegalaxies (ETGs). We use the GALFORM model of galaxy formation, set in the$\Lambda$ cold dark matter framework, and coupled it with a Monte-Carlosimulation to follow the angular momenta flips driven by matter accretion ontohaloes and galaxies. We consider a gas disk to be misaligned with respect tothe stellar body if $\alpha_{\rm G,S}>30$~degrees. By assuming that the onlysources of misaligments in galaxies are galaxy mergers, we place a lower limitof $2-5$ per cent on the fraction of ETGs with misaligned gas/stellarcomponents. These low fractions are inconsistent with the observed value of$\approx 42\pm 6$ per cent in ATLAS$^{\rm 3D}$. In the more general case, inwhich smooth gas accretion in addition to galaxy mergers can drivemisalignments, our calculation predicts that $\approx 46$ per cent of ETGs have$\alpha_{\rm G,S}>30$~degrees. In this calculation, we find correlationsbetween $\alpha_{\rm G,S}$ and stellar mass, cold gas fraction and starformation rate, such that ETGs with high masses, low cold gas fractions and lowstar formation rates are more likely to display aligned cold gas and stellarcomponents. We confirm these trends observationally for the first time usingATLAS$^{\rm 3D}$ data. We argue that the high fraction of misaligned gas discsobserved in ETGs is mostly due to smooth gas accretion (e.g. cooling from thehot halo of galaxies) which takes place after most of the stellar mass of thegalaxy is in place and comes misaligned with respect to the stellar component.Galaxies that have accreted most of their cold gas content prior to the timewhere most of the stellar mass was in place show aligned components.

The origin of the atomic and molecular gas contents of early-type galaxies. II. Misaligned gas accretion