I've got an idea partially birthed and I need help finishing it. Why would a dragon require a rider with the ability to sense and use magic but other mythological beasts would not? A bit of background: My story focuses on the Beast Riders, a group of fighters who ride mythological beasts such as pegasus, gryphon, hippogriffs, unicorn, and a couple other I've made up. All the Beasts have some sort of magical ability, thanks to the High Magic concentrated in the area where they are born and raised (the Beast Preserve). Most riders do not. High Magic is mostly concentrated in the neighboring country, Esharia. MC's mother was Esharian, with wizarding blood in her family. MC's father comes from the Dragon Bloodline. (something I have to develop further). His great-grandmother was Esharian, and his grandfather the last Rider with a dragon mount. So it is only when the Dragon Bloodline combines with someone who can sense/use High Magic that it is even possible for that person to get a dragon mount. (I'll go into mount selection if you ask, but I'm not going to do it right here bc I don't want to bore you/give info overload) I just need to figure out why.
Short answer: Who cares... no, seriously. Hand wave it. It sounds as if you have enough explanation and narrative weight dedicated to this already, so why slog through more for something that isn't terribly important? Or, just say that dragons are special. Like humans, they won't let anybody climb up and ride them.
You could make the dragons "children of a lesser/different god" like the Dwarves of Middle Earth. Their connection with magic could be from a different source, a different manner of engagement. You could use it as part of your setting. The other creatures have a particular connection, familiarity, understanding with one another, but not with dragons. Even the fierce hippogriffs never turn their backs on them. The magic is there. They feel it. But it's a different current, a different flavor, a different color. You could take that in any direction you wanted. It makes the pairings of human and dragon of greater respect, of suspicion to the other pairings, both, anything you want.
Ooh. What if, long ago, the dragons and those humans of the dragon bloodline originally came from a different place. Different continent, now forgotten, or different world even, via a portal or something. They used a slightly different kind of magic. Over time, the human descendants lost their ability to use the old magic due to interbreeding. But Esharia's High Magic has a similar "flavor"...so when a child is born who has dragon bloodlines and high magic bloodlines, they 'feel' familiar to the dragons, like the humans they used to know and love...and that's why the dragons allow them as riders.
I saw the word dragons and rushed to the thread but I see I'm not needed here. Wreybies pretty much nailed it. Good luck!