We study the hadronic D meson decays into a pseudoscalar meson P and an even-parity meson M, where M represents a scalar meson S, an axial-vector meson A, or a tensor meson T. These decays are first analyzed in the flavor-diagram approach. Fits to the SP modes with S being a nonstrange scalar meson show that neither the simple q (q) over bar picture nor the q(2)(q) over bar (2) scheme is favored by data. Current measurements on the AP decays are insufficient for a meaningful analysis. Some TP data are inconsistent with the others. In certain cases, the W-annihilation diagrams indicated by the data are unexpectedly large. As a comparison, we also compute their decay rates in the factorization approach using form factors extracted from the covariant light-front model. We find that factorization works well for Cabibbo-allowed D(+) -> SP, AP decays free of the weak annihilation contributions (W-exchange or W-annihilation). For the other SP and AP modes, it is necessary to include weak annihilation contributions to account for the data. However, factorization fails for D -> TP decays for some unknown reason; the predicted rates are in general too small by at least 2 orders of magnitude compared to experiment. We also examine the finite-width effects of resonances. Some decay modes which are kinematically forbidden become physically allowed due to the finite width of the resonance. We show that the branching fraction of D(+) -> sigma pi(+) extracted from three-body decays is enhanced by a factor of 2, whereas B(D(0) -> f(2)(1270)(K) over bar (0)) is reduced by a factor of 4 by finite-width effects.