ABSTRACT The similarity between the distributions of spins for galaxies (λgal) and for dark-matter haloes (λhalo), indicated both by simulations and observations, is naively interpreted as a one-to-one correlation between the spins of a galaxy and its host halo. This is used to predict galaxy sizes in semi-analytic models via Re ≃ fjλhaloRvir, where Re is the half-mass radius of the galaxy, fj is the angular momentum retention factor, and Rvir is the halo radius. Using two suites of zoom-in cosmological simulations, we find that λgal and the λhalo of its host halo are in fact barely correlated, especially at z ≥ 1, in line with previous indications. Since the spins of baryons and dark matter are correlated at accretion into Rvir, the null correlation in the end reflects an anticorrelation between fj and λhalo, which can arise from mergers and a ‘wet compaction’ phase that many high-redshift galaxies undergo. It may also reflect that unrepresentative small fractions of baryons are tapped to the galaxies. The galaxy spin is better correlated with the spin of the inner halo, but this largely reflects the effect of the baryons on the halo. While λhalo is not a useful predictor for Re, our simulations reproduce a general relation of the form of Re = ARvir, in agreement with observational estimates. We find that the relation becomes tighter with A = 0.02(c/10)−0.7, where c is the halo concentration, which in turn introduces a dependence on mass and redshift.