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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, the main feature of which is the presence of a population of the demagnetized electrons in a magnetic field with a very small normal component Bn, and show that the free parameters of this model, such as the relative part of demagnetized electrons, their incoming 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 electron tearing modes, which are an order of magnitude faster and have shorter wavelengths than the ion modes in ion-scale TCSs. This work was supported by Russian Science Foundation (grant 23-12-00031)