Most climate models show a poleward shift of the southern hemispheric zonal-mean jet in response to climate change, but the inter-model spread is large. In an attempt to constrain future jet responses, past studies have identified an emergent constraint between the climatological jet latitude and the future jet shift in austral winter. However, we show that the emergent constraint only arises in the zonal mean and not in separate halves of the hemisphere, which questions the physicality of the emergent constraint. We further find that the zonal-mean jet latitude does not represent the latitude of a zonally coherent structure, due to the presence of a double-jet structure in the Pacific region during this season. The zonal asymmetry causes the previously noted large spread in the zonal-mean climatology but not in the response, which underlies the emergent constraint. We therefore argue that the emergent constraint on the zonal-mean jet cannot narrow down the spread in future wind responses, and we propose that emergent constraints on the jet response in austral winter should be based on regional rather than zonal-mean circulation features.