The pairing with Parashah Haazinu, whose entire content is Moses's own extended poetic song reviewing God's faithfulness across Israel's history and foretelling both future unfaithfulness and eventual restoration, rests on the clearest possible genre match available in the haftarah cycle: both readings are lengthy poetic songs composed by a single towering leader, delivered near the end of that leader's own life or career, recounting God's past deliverance in vivid, elevated language rather than in ordinary narrative prose.
Where Moses's song looks primarily forward, warning of a future the nation has not yet lived through, David's song looks primarily backward, celebrating deliverances he has already personally experienced across a long and eventful reign, so that the two songs, read together, offer complementary temporal perspectives on the same underlying relationship between God and God's chosen leader.
Both songs also share vivid natural and cosmic imagery to convey God's power, Moses's song describing God as a rock and comparing Israel's history to the growth and decline of a nation under divine care, and David's song describing earthquakes, smoke and fire accompanying God's direct intervention, a shared poetic vocabulary of overwhelming natural force used to describe what ordinary narrative language alone could not adequately convey.