Kesterite solar cells show the highest efficiency when the absorber layers (Cu ZnSnS [CZTS], Cu ZnSnSe [CZTSe] and their alloys) are non-stoichiometric with Cu / (Zn + Sn) ≈ 0.8 and Zn / Sn ≈ 1.2. The fundamental cause is so far not understood. Using a first-principles theory, we show that passivated defect clusters such as Cu + Sn and 2 Cu+ Sn have high concentrations even in stoichiometric samples with Cu/(ZnSn) and Zn/Sn ratios near 1. The partially passivated Cu+ Sn cluster produces a deep donor level in the band gap of CZTS, and the fully passivated 2Cu+ Sn cluster causes a significant band gap decrease. Both effects are detrimental to photovoltaic performance, so Zn-rich and Cu, Sn-poor conditions are required to prevent their formation and increase the efficiency. The donor level is relatively shallower in CZTSe than in CZTS, which gives an explanation to the higher efficiency obtained in Cu ZnSn (S, Se) (CZTSSe) cells with high Se content.