In this paper we attempt to provide a theoretical explanation of the observed approximate pressure isotropy in the near-earth geomagnetic tail. We first give a new formulation of the self-consistent theory of two-dimensional anisotropic steady states by generalizing the Grad--Shafranov equation. Then it is shown that anisotropy-driven instabilities, active in the midplane of the plasma sheet, lead to highly isotropic pressure tensors for the entire plasma sheet. The key point is that due to the weakness of the magnetic field in the midplane the instabilities require only a small pressure anisotropy to be excited. The approach is based on the assumption that an originally unstable system evolves into a steady state. An order of magnitude analysis is supplemented and confirmed by a numerical example.