Cortical excitatory (E) neurons exhibit clear tuning to stimulus features, but the tuning properties of inhibitory interneurons remain ambiguous. While inhibitory neurons are traditionally viewed as functionally and structurally untuned [1-4], recent studies indicate that parvalbumin-expressing (PV) neurons do show feature selectivity and establish co-tuned reciprocal connections with individual pyramidal neurons at a pairwise level [5-7]. Using mean-field theory and large-scale network simulations of spiking cells (Fig. 1A), we reconcile these seemingly contradictory findings by demonstrating that at the single-cell and pairwise level, both types of experimental findings are valid as they emerge in our simulations. In fact, our results demonstrate that at the single-cell level, PV cells project more strongly onto E cells with stronger reciprocal projections (Fig. 1D-F), confirming the presence of pairwise co-tuning. However, our analysis indicates that this does not preclude the absence of functional and structural tuning of inhibitory cells at the single-cell level, as reciprocal motifs with correlated E and PV synaptic strength also exist among pairs that are tuned to opposite features (Fig. 1G,H). To elucidate the origins of co-tuning in PV interneurons and their significance at the network level, we employ mean-field theory to calculate the average PV-to-E IPSP evolution in networks composed of 2 E and 1 PV assemblies. We find a combination of homeostatic plasticity governing PV-to-E connections (Fig. 1B), heterogeneity in excitatory postsynaptic potentials (EPSP) impinging on PV neurons (Fig. 1C), and shared correlated input from higher cortical areas to E cells (Fig. 1A) leads to the functional and structural self-organization of PV subnetworks. Removing any of these components disrupts PV co-tuning to E cells. Notably, a more heterogeneous distribution of EPSP from E to PV cells enhances functional and structural co-tuning (Fig. 1C,D), highlighting the importance of collective connectivity from E to PV cells. Our findings reveal that population-level measures identify functional (Fig. 1H, right) and structural (Fig. 1G, right) co-tuning of PV neurons, which are not evident in pairwise (Fig. 1H, left) and individual-level measures (Fig. 1G, left). This emphasizes the role of E-to-PV EPSP heterogeneity in shaping PV cell co-tuning and highlights the utility of population-level measures in identifying structural and functional tuning of cell types.