Recent MMS observations have discovered electron‐scale super‐thin current sheets (STCSs) with a partial electron demagnetization, which distinguishes them from the ion‐scale TCSs traditionally observed by the Cluster mission. Our investigation focuses on the dynamics of STCSs and reveals new aspects influencing their stability. We use the earlier proposed 1D collisionless self‐consistent equilibrium STCS model and show that the free parameters of this model, such as the relative part of demagnetized electrons, their flow velocity and the pressure anisotropy of magnetized electron population, can contribute to the development of tearing instability. With the growth of these parameters, the STCS becomes thinner, which leads to the accumulation excess of a free energy. Stabilizing energy decreases due to the increase of a relative part of demagnetized electrons. Thus, demagnetized electrons in STCSs can provide the development of fast and short‐wavelength electron tearing modes. Plain Language Summary Recent MMS observations in space plasma have discovered extremely thin current sheets having the transverse electron scales. These sheets are different from the thicker current sheets usually observed by the Cluster mission. The electrons in these sheets are partially demagnetized, that is, they are not affected by magnetic fields. The presence of demagnetized electrons can lead to the development of a fast tearing mode with the shorter wavelengths in comparison with corresponding modes observed in the thicker current configurations. Our investigation focuses on the understanding of the dynamics of these super‐thin current sheets and the identification of factors that influence their stability. Key Points Demagnetized electrons supporting STCSs can initiate the fast electron tearing instability at short wavelengths Fast growth of small‐scale magnetic perturbation results in the formation of magnetic islands, that is, plasmoids Development of fast tearing mode is followed by strong inductive electric fields