Although Bregman-type algorithms have been extensively studied over the years, it remains unclear whether existing stationarity measures, often based on Bregman divergence, can distinguish between stationary and non-stationary points. In this talk, we answer this question in the negative. Furthermore, we show that Bregman-type algorithms are unable to escape from a spurious stationary point in finite steps when the initial point is unfavorable, even for convex problems. Our results highlight the inherent distinction between Euclidean and Bregman geometries and call for further investigation of Bregman-type algortihms.