The semi-empirical mass formula's pairing term is attractive only for even-even nuclei, see for example, Miriam Hein et al. 2022$2022$ Eur. J. Phys. 43 035801$43$ $035801$. That is, it is pairing between protons or pairing between neutrons. This is the isospin T=1$T=1$ channel, where the S=0$S=0$ interaction is most attractive. Your statement that S=1$S=1$ is most attractive is true for T=0$T=0$ i.e. the deuteron channel, but this is not the pairing contained in the semi-empirialempirical mass formula term.
