Within an attempt to unravel the conundrum of irregular bandgap variations in hybrids of white-graphene (hBN) and graphene (G) observed in both experiment and theory, strong proofs about the decisive role of aromaticity in their electronic properties are brought to light. Sound numerical experiments conducted on zero-, one- and two-dimensional hBNG hybrids demonstrate that upon structural and/or electronic perturbation caused by foreign doping agents, the uniformity in local cyclic electron delocalization of ideal graphene restructures locally creating carbon hexagons of contrasting cyclic electron delocalization (c.c. local aromatic patterns) which may dominate the bandgap size of the resulting systems. In addition, relying on the quantum chemical aspect of aromaticity in terms of quantitative computations of cyclic electron delocalization together with pictorial intrinsic polarizability density representations, this work provides a solid and handy rule-of-thumb to be used in qualitative and intuitive predictions. According to this empirical rule, the origin of any nonmonotonic bandgap variation observed in stoichiometric 0D (BN)_n/graphene hybrids with increasing hBN segment lies in instabilities caused by partially substituted benzenoid rings formed locally at the hBNG interfaces. This relationship, established in 0D graphene flakes and extended to 1D periodic ribbons, can be used to understand and qualitatively predict conflicting bandgap variations of vacancy-free 2D periodic lattices, pointing at the property of aromaticity as the missing link needed to solve the puzzle of conflicting bandgap variations in hBNG hybrids observed in experiment.