Tropical precipitation in climate models presents significant biases in both the large-scale pattern (i.e., double Intertropical Convergence Zone bias) and local-scale characteristics (i.e., drizzling bias with too frequent drizzle/convection and reduced occurrences of no and heavy precipitation). By untangling the coupled system and analyzing the biases in precipitation, cloud and radiation, this study shows that local-scale drizzling bias in atmospheric models can lead to large-scale double-ITCZ bias in coupled models by inducing convective-regime-dependent biases in precipitation and cloud radiative effects (CRE). The double-ITCZ bias consists of a hemispherically asymmetric component that arises from the asymmetric SST bias and a nearly symmetric component that exists in atmospheric models without the SST bias. By increasing light rain but reducing heavy rain, local-scale drizzling bias induces positive (negative) precipitation bias in the moderate (strong) convective regime, leading to the nearly symmetric wet bias in atmospheric models. By affecting cloud profile, local-scale drizzling bias induces positive (negative) CRE bias in the stratocumulus (convective) regime in atmospheric models. Because stratocumulus (convective) region is climatologically more pronounced in the southern (northern) tropics, the CRE bias is deemed to be hemispherically asymmetric and drives warm and wet (cold and dry) biases in the southern (northern) tropics when coupled to ocean. Our results suggest that correcting local-scale drizzling bias is critical for fixing large-scale double-ITCZ bias. The drizzling and double-ITCZ biases are not alleviated in models with mesoscale (0.25~0.5^o) or even storm-resolving (~3km) resolution, implying either large-eddy simulation or fundamental improvement in small-scale subgrid parameterizations is needed.