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ABSTRACT The correlations between supermassive black holes (SMBHs) and their host galaxies still defy our understanding from both the observational and theoretical perspectives. Here, we perform pairwise residual analysis on the latest sample of local inactive galaxies with a uniform calibration of their photometric properties and with dynamically measured masses of their central SMBHs. The residuals reveal that stellar velocity dispersion $$\sigma$$ and, possibly host dark matter halo mass $$M_{\rm halo}$$, appear as the galactic properties most correlated with SMBH mass, with a secondary (weaker) correlation with spheroidal (bulge) mass, as also corroborated by additional machine learning tests. These findings may favour energetic/kinetic feedback from active galactic nuclei (AGNs) as the main driver in shaping SMBH scaling relations. Two state-of-the-art hydrodynamic simulations, inclusive of kinetic AGN feedback, are able to broadly capture the mean trends observed in the residuals, although they tend to either favour $$M_{\rm sph}$$ as the most fundamental property, or generate too flat residuals. Increasing AGN feedback kinetic output does not improve the comparison with the data. In the Appendix, we also show that the galaxies with dynamically measured SMBHs are biased high in $$\sigma$$ at fixed luminosity with respect to the full sample of local galaxies, proving that this bias is not a by-product of stellar mass discrepancies. Overall, our results suggest that probing the SMBH–galaxy scaling relations in terms of total stellar mass alone may induce biases, and that either current data sets are incomplete, and/or that more insightful modelling is required to fully reproduce observations.