It's not that I dislike socializing — I'm just tired.

Literal

Socializing [subject-が] unpleasant reason [copula-ではない] [but-が] tired [explanatory-のだ].

~わけではないが~のだ is a two-part pattern: 'it's not that X, but (the real reason is) Y.' 付き合い = 'socializing/social obligations.' のだ gives explanatory force to the real reason.