The lines of critical points of rare-gas binary mixtures are evaluated within the framework of a statistical mechanics theory of thermodynamic stability, recently developed by Chen and Forstmann. The phase instabilities an related to the local compositional and density order in the fluid through a density functional expansion of the grand canonical potential. The structural inputs are determined by using the thermodynamically self-consistent integral equation scheme known as hypernetted chain/mean spherical approximation (HMSA). A good agreement is obtained with neutron scattering data of He-Xe and Ne-Xe mixtures near the phase transition. Although the accuracy in reproducing the experimental critical point lines is only semi-quantitative, the qualitative behaviors are properly described. For the first time, a detailed microscopic interpretation of the so called behavior of the "second type" of the critical line is given.