During primary neurulation in amniote embryos, the neural plate gives rise to the neural tube in a process requiring the coordination of forces at different scales throughout a geometrically complex tissue. The ways in which this process fails inform us of the complex mechanical conditions required for its correct completion. Previous results showed that the functional disruption of MARCKS, a protein which simultaneously interacts with the plasma membrane and actin filaments, resulted in neural tube closure defects with apical cell extrusion. Here, we show that this is an example of “live cell extrusion”, wherein extruded cells are not undergoing apoptosis. This suggests that extrusion in this case might be due to a mechanical instability in the neural plate. Using an expanded energy-based vertex model of pseudostratified epithelia we then show that extrusion may be elicited by a reduction in the relative surface tension of apical and basal interfaces with respect to cell-cell interfaces. Finally, by considering a continuum description of a simplified epithelium we derive an approximate quantitative threshold for single-layered epithelial stability in the form of a power law relating cell density to the relative value of interfacial surface tensions. Our work serves to explain an example of how alterations in polarization and forces at the single-cell level can produce tissue-scale instabilities which not only greatly alter its morphology but can also ultimately lead to severe developmental defects.