The traditional photon absorbers Cu2-xX (X = S, Se, and Te) have regained significant research attention in the search of earth-abundant photovoltaic materials. These moderate- and narrow-gap materials have also been shown to exhibit excellent thermoelectric properties recently. However, semimetallic band structures with inverted band orderings are predicted for antifluorite structure Cu2X using density functional theory with the local density approximation or the generalized gradient approximation. We find that semiconducting band structures and normal band orderings can be obtained using the modified Becke-Johnson potential plus an on-site Coulomb U (the mBJ+U approach), which is consistent with our earlier finding for diamond-like Cu-based multinary semiconductors [Y. Zhang, J. Zhang, W. Gao, T. A. Abtew, Y. Wang, P. Zhang, and W. Zhang, J. Chem. Phys. 139, 184706 (2013)]. The trend of the chemical bonding of Cu2X is analyzed, which shows that the positions of the valence band maximum and conduction band minimum are strongly affected by the inter-site pd and intra-site sp hybridizations, respectively. The calculated gaps of Cu2S and Cu2Se still seem to be underestimated compared with experimental results. We also discuss the effects of different structural phases and Cu disordering and deficiency on the bandgaps of these materials.