The origin of the instability of the normal state of electrons in the superconducting copper oxides is shown by the K-J model, in which the superexchange (K) between local moments and the Kondo exchange ( J) between electron and local moment are considered. The suppression of superexchange via impurity doping may induce effective spin coupling between electrons and triplet pairing (S = 1, Sz = 0). The spin pairing theory explains the phase diagram of high-To superconductors, especially the superconducting transition temperature Tc, the pseudogap temperature T* and the magnetic crossover temperature Tn as a function of the doped hole concentration. The universal expression for the empirical law of the superconducting transition temperature is derived from the theory.