Why did Deoxys come to Earth?

I don't know how they extrapolated it. Groudon/Kyogre came out 3000 years, 2000 years before, it was the meteoroid. There was no mention of what happened 1000 years after that? Though I do recall the dialogue where they were talking about the cyclical events of Hoenn.

3000 years ago: "In the face of Primal Groudon and Kyogre's great power, people could do nothing. The only choice was to watch as disaster upon disaster swept over them. It was in such a time that a great many meteoroids poured from the darkness of space, from a place higher even than the heavens. And the meteoroids fell in their multitude upon a waterfall that had long been home to a tribe of Dragon-type-Pokémon users... The meteors shone with a rainbow brilliance, as if some great life was held within. That was when, as if drawn by the brilliance, a Pokémon that shone in a blazing emerald hue descended from the heavens... That Pokémon was none other than Rayquaza. Rayquaza’s power overwhelmed that of the two Primal Pokémon, and peace returned to the world. The people of Hoenn revered Rayquaza as a true savior."

2000 years ago: "A thousand years after this time, the meteoroids once again fell. A huge meteoroid, far greater than any before, struck the planet, boring deep into the ocean and leaving behind it a crater larger than any other. The land born of this event later become known as Sootopolis. The great meteoroid was the first of many disasters to befall humanity. When it punched into the planet, the land cracked beneath it, and a great welling of natural energy poured from beneath Hoenn. Thirsting for that energy, Primal Kyogre and Primal Groudon once again woke. The people had a wish—a memory from a thousand years before... They wished that the Legendary Pokémon clad in emerald light would appear again. The huge Meteorite that lay at the heart of Sootopolis gave off a boundless brilliance. In its brilliance, it resembled a vast and powerful Key Stone. And once again, Rayquaza descended from whence it came in the heavens. The people fell to their knees before Rayquaza and made a wish for salvation. As they did, a great change came over the Legendary Pokémon. It was enveloped in blinding light. As the light receded, they beheld a Rayquaza beyond all knowledge— a sublime figure, incandescent with overwhelming life force. It was humanity’s wish that brought about Rayquaza’s transformation in the face of the rainbow stone..."

1000 years ago: "A thousand years of peace followed after that disastrous time. But the Draconid people, learning from their long history’s cyclical nature, foretold that the meteoroids would fall on this land again. The meteoroid to come, they prophesized, would be far greater than those that had come before it. This meteoroid would be great enough to break the world forever... In order to prevent this great calamity, those who held the knowledge of the past arrived at a plan. Their plan was to invoke Rayquaza, the great savior, and summon it to this land before the meteoroid could strike."

Chances are that there were similar events going even further into the past, except without Mega Rayquaza.