We demonstrate an unusual behavior of a practically-important reaction of selective catalytic reduction (SCR) of NOx with NH3 over a state-of-the-art Cu-SSZ-13 catalyst. In response to increasing temperature, the rate of SCR reaction increases initially, attains a maximum around 300 degrees C, and then declines, resulting in a negative apparent activation energy at higher temperatures. This behavior has never been previously reported because the side reaction of NH3 oxidation obfuscated the kinetic analysis of SCR reaction at high temperatures. We were able to discover this phenomenon by performing severe hydrothermal aging of the catalyst that suppressed the NH3 oxidation activity without a significant change in the SCR activity. Further, we show that the phenomenon is more general and also found in other Cu- and Fe-exchanged zeolite and V2O5-(WO3)/TiO2 catalysts. The behavior is explained based on the fact that the activation energy for NH3 desorption is higher than that for standard SCR reaction. Therefore, at higher temperatures, the increase in the SCR reaction rate constant with temperature gets outpaced by the decline in the NH3 coverage, resulting in the overall decline of the reaction rate. One of the implications of the finding is that the studied Cu-SSZ-13 SCR catalyst never operates in a purely external mass transfer limited regime, under the range of conditions relevant to the practical SCR applications. In other words, there is always a certain contribution of slower reaction rate to the performance of the SCR catalyst, even after increasing the reaction rates by increasing catalyst amount, using the "fast" SCR reaction, or operating at elevated temperatures. This has significant consequences for the design of practical SCR catalysts, in particular related to the choices of the active material loading and channel hydraulic diameter, as empirically and analytically demonstrated in this paper.