I have a silly confusion. The Pairing term of the semi-empirical mass formula tells that nucleons tend to pair up. I believe that pairing up means forming a state in which two nucleons combine to give a total $S=0$ (or total $J=0?$). Pairing increases the binding energy.
On the other hand, we know that nuclear forces favour the alignment of spin i.e. $S=1$ is favoured over $S=0$.
Don't these two statements contradict each other and say completely opposite things?