While the surface termination of quasi-spherical metal chalcogenide nanocrystals or quantum dots has been widely investigated, it remains unclear whether the ensuing surface chemistry models apply to similar nanocrystals with anisotropic shapes. In this work, we report on the surface-chemistry of 2D CdSe nanoplatelets, where we make use of an improved synthesis strategy that yields stable and aggregation free nanoplatelet suspensions with a photoluminescence quantum yield as high as 55%. We confirm that such nanoplatelets are enriched in Cd and, by means of 1H nuclear magnetic resonance spectroscopy, we show that the Cd-rich surface is terminated by X-type carboxylate ligands. Not unlike CdSe quantum dots (QDs), entire cadmium carboxylate entities can be displaced by the addition of amines, and the desorption isotherm points toward a considerable binding site heterogeneity. Moreover, we find that even the slightest displacement of cadmium carboxylate ligands quenches the nanoplatelet photoluminescence. These experimental findings are further confirmed by density functional theory (DFT) calculations on a 5 monolayer model CdSe nanoplatelet. These simulations show that the most labile ligands are located in the vicinity of facet edges, and that the displacement of ligands from such edge sites creates midgap states that can account for the observed photoluminescence quenching. Next to extending surface chemistry insights from colloidal QDs to nanoplatelets, this work indicates that CdSe nanoplatelets constitute a unique nanocrystal model system to establish a comprehensive description of midgap trap states, which includes their structural, chemical, and electronic properties.