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