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In the absence of Arceus (the guiding hand) or Giratina (the mutual foe) Dialga and Palkia are forced into conflict when their territories overlap. Base reality is an amalgam of spacetime but Dialga and Palkia are capital T Time and capital S Space, the literal embodiment of each metaphysical concept. They are not just stewards of their respective concepts, they function more like gods with Time and Space as their divine spheres.
When the two realms collide outside of reality, conflict ensues. Both concepts are essentially selfish in nature, which befits their role as the absolute incarnation of their respective element. Palkia / Physical Matter will be ultimately defeated by the infinite march of time, so it is in its best interest to slay Dialga and create an boundless world of terrain with no distinction between Past, Present, and Future. For Dialga’s part, the presence of “Space” makes Time unwieldy and more taxing for it to manipulate correctly. Dialga’s ideal universe would be a realm of pure time which might resemble some sort of fourth dimensional construct rather than a conventional terrestrial universe. It would be even more unrecognizable than Palkia’s paradise (a place where nothing changes or has ever changed).
Obviously both options are bad for humanity / Pokemon, and Arceus clearly favors humanity / Pokemon so the Big God steps in to smack the little Gods around whenever they step out of line.