We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ2× T2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and N = 1 supersymmetric SU(N) Yang-Mills theory.