Comprehensive climate models fail to capture historical sea surface temperature (SST) trends in the Southern Ocean, where multidecadal cooling occurred despite global warming. Efforts to explain this discrepancy have invoked underestimated mixed-layer freshening, which produces cold SST anomalies through enhanced stratification. However, single-model freshwater forcing experiments have produced a wide range of SST responses, and the relative importance of different freshwater sources remains unclear. To address these ambiguities, this study quantifies linear SST response functions for standardized freshwater flux increases across CMIP6 models and estimates the 1990-2021 SST cooling from observed freshwater inputs. We attribute the lack of SST cooling trends in CMIP6 to missing Antarctic Ice Sheet meltwater and underestimated precipitation increases, each producing similar 1990-2021 cooling tendencies. Adjusting SST trends for these missing sources improves model-observation agreement, quantifying, for the first time, the impact of missing freshwater forcing on Southern Ocean SST trends across a multi-model ensemble.