Generic statements like *A dog has four legs* are central to encode general knowledge. Yet their form–meaning mapping remains elusive. Some predicates sound natural with indefinite singulars (*a*-generics), while others require the definite article (*the*-generics) or the bare plural (bare-plural generics). For instance, why do we say *The computer revolutionized education* but not *A computer revolutionized education*? We propose a construction-based account explaining why not all generic statements are created equal. Prior accounts invoke semantic notions like kind-reference, stage-levelness, or accidental generalization, but offer no unified explanation. This paper introduces a new explanatory dimension: predicate collectivity level, i.e. whether the predicate applies to each member of a group or to the whole group as a unit (without necessarily applying to each of its members individually). Using two preregistered acceptability experiments we show that *a*-generics, unlike *the*-generics and bare-plural generics, are dispreferred with collective predicates. The findings offer a functionally motivated, empirically supported account of morphosyntactic variation in genericity, providing a new entry point for Construction Grammar.