There are many different species that we come across in the Artemis Fowl universe. Let's take a few examples: elves, humans, and demons. Oh, and centaurs.
We know that elves have magic, and, as far as we know, always have. Holly Short is our example of an elf.
Now, for humans. Humans once had their own magic but forgot how to use it:
He felt the magic ignite in his nerve endings, filling him up, elevating his consciousness to another place. It was a euphoric experience. Artemis realized there were sections of his brain opening up that hadn't been used by humans for millennia. He also realized that humans must have had their own magic once, but had forgotten how to use it.
Artemis Fowl: The Lost Colony, chapter 15: "Home Again, Home Again"
Demons are a bit special. They came from the moon, and only the warlocks have magic, but not most demons. And demons aren't native to Earth, they developed from moon creatures.
Since the warlocks had been explosively removed from the 8th Family, nobody had much of a clue about magic anymore. Normal demons had no magic of their own. It had been thought that all the warlocks had been sucked into space during the transferal of Hybras from Earth to Limbo...
Artemis Fowl: The Lost Colony, chapter 3: "First Impression"
And finally, Foaly informs us that centaurs don't have any magic.
One shot and it was all over. Centaurs didn't have magic. Not a drop. They got by on brains alone. That and their ability to trample their enemies underfoot. But Foaly had a feeling that Briar wouldn't plug him just yet. Too busy gloating.
Artemis Fowl: The Arctic Incident, chapter 9: "No Safe Haven"
Why do all of these species have different levels of magic like this, in-universe?