We’re clearly referred to as owners on the site, and neopets are called our pets, so here’s the only reasonable explanation:

Sometime in our very distant future, but in Neopets’ very distant past, space ships full of human beings looking for a new home landed in Neopia Central and, because of the talking animal’s resemblance to the pets we knew and loved, the humans enslaved all the neopets they found there. However, they did this not out of cruelty but care, believing that this was the best way to protect neopets from harmful enemies and themselves.

Those were the dark days, where humans would travel through the lands and collect new exotic neopets for their collection. We conditioned them to love us then trained them to fight on our behalf. Free neopets, refusing to fight against their own, could only protect their lands as best they knew how. The faeries, then ruled by Queen Fyora’s mother, were reluctant to sacrifice themselves and their magic for the neopets, for they too were vulnerable to being bottled and enslaved. So they kept to themselves in their home among the clouds.

Years passed and though some revolutions were started and battles were fought, no force could shake the human’s hold on the neopets. Moreover, the first generation of slaves gave birth to a new generation, and one after that, each more conditioned to believe that true satisfaction as a neopet only came when looked after by a loving owner. This belief became close to a religion and the neopet slaves - or pets as they preferred to be called - were satisfied with their lives.

Then Queen Fyora came in to power and could not stand to see such enslavement within the planet. She gathered allies throughout the other lands until she amassed a force that could threaten to overwhelm the alien slave-drivers. She threatened the humans with an ultimatum: release the slaves or face destruction. The humans reluctantly released their pets.

But none of them left. In fact, most begged to say. Even those trapped in their pounds (which, like their shops and other facilities, were run by free neopets with no moral conscience, yes even the adoption uni) would rather sit and wait for an owner to find them and fulfill their lives than be released to terrifying independence.

Queen Fyora was forced to relent but gave the following decree: humans could no longer enslave new neopets. All pets must have been bred in slavery (Draik eggs included, shops would never stock the offspring of free draiks) and all were free to leave if they chose to do so.

And so it was.

But there were more pets than owners and the humans felt an obligation to their slaves so they sent for their brethren. That’s when we arrived in neopia central on space ships, chose our pets/slaves, and explored the land as if it were a new world - which it was, to us.

Queen Fyora and all the free neopets learned to accept us, for we made valuable contributions to their society. We defended them in their wars and helped to solve their puzzles, we provided valuable trade of goods from one land to the next, ensuring exotic foods from shenkuu could be sold in our own shops which numbered in the thousands around the world.

When new neopets were discovered, Queen Fyora always worried that we, the humans, would revert to our old kidnapping ways. But we didn’t need to. Attracted by our pet’s contentment, their sincere belief that fulfillment only came through finding a loving human home, they came of their own free will to Neopia Central and asked to become pets.

tl;dr: we’re alien slavers who kidnapped our neopet pet’s ancestors and bred a cult of neopets that believed only through slavery they could find contentment.