In recent years, to meet the demand for high-gain beam-scanning antennas, low-cost 1-bit reconfigurable array antennas have been proposed, such as the reconfigurable reflectarray antennas (RRAs), RRAs with polarization conversion (PC-RRAs), reconfigurable transmitarray antennas (RTAs), RTAs based on near-field feeding method (NF-RTAs), planar reconfigurable array antennas (PRAAs) and so on. Interestingly, with the exception of RRAs, all of these 1-bit reconfigurable elements require a minimum of two switches to achieve a 180° phase difference. This paper utilizes a three-port microwave network to model the single-switch reconfigurable array antennas and demonstrates through contradiction that achieving both high scattering amplitude and 180° phase shifting range for single-switch PC-RRA, RTA, NF-RTA, and PRAA elements is not feasible. This proof is significant for the theory and design of the reconfigurable array antennas.