The Altland-Zirnbauer classification of random matrices is based on three symmetries: time-reversal, charge conjugation, and a third which is sometimes referred to as "chiral" or "sublattice" symmetry, which is satisfied when a unitary matrix $\Omega$ exists that anticommutes with the Hamiltonian. This usage seems to have very little to do with the concept of chirality in relativistic quantum field theories (the chirality operator $\gamma^5 = i\gamma^0\gamma^1\gamma^2\gamma^3$ commutes with the Hamiltonian of a massless fermion and anticommutes with a mass term $m\gamma^0$). Where did this terminology originate?
EDIT: I am not asking why chiral symmetry is a symmetry or what it means (according to wikipedia it comes from the greek word for 'hand' which is appropriate because it refers to left or right handedness in most contexts). The question is what does this have to do with the definition of chiral symmetry used for the Altland-Zirnbauer classification of random matrices, i.e. a unitary operator which anticommutes with the single particle Hamiltonian. The most basic model this shows up in is the SSH model, where it has nothing to do with left or right handedness. I want to know where this language comes from. This is not a question about physics, it's a question about the origin of terminology used in a specific area of physics. The meaning in field theory contexts is clear to me, so I would appreciate answers which refer to random matrices or the periodic table of topological invariants. I am unable to find any papers or textbooks which explain this terminology and all the experts in the field I have spoken to say they do not know where it came from and heavily prefer the term "sublattice symmetry" specifically in order to avoid confusion with the meaning of chiral symmetry in other contexts. If the use of terminology seems to be so unrelated to its obvious meaning to the extent that people avoid such usage due to possible confusion, why did people use it in the first place?