A salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the typeābcd, with four different quark flavors. This phenomenon may be understood from the properties of large-Nc QCD: On the one hand, consistency conditions for flavorexotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks TA and TB: each of them should decay dominantly via a single two-meson channel, TA →On the other hand, we have at hand only one diquark-antidiquark flavor structure (āc)(bd) that might produce a compact tetraquark bound state. Taking into account that the diquark-antidiquark structure is the only viable candidate for a compact tetraquark state, one concludes that it is impossible to have two different narrow tetraquarks decaying dominantly into different two-meson channels. This contradiction suggests that large-Nc QCD does not support the existence of narrow flavorexotic tetraquarks. This argument does not rule out the possible existence of broad molecular-type flavor-exotic states, or of molecular-type bound states lying very close to the two-meson thresholds.