Anyways, yeah, D&D does have a weird thing about half-elves, half-orcs, half dwarves and half-everything under the sun. I guess there is that either that percentage of the market base that can't commit to the weird archtypes of a fantasy race, but doesn't want to play a plain ol' boring human, or the types that gotta imagine crazy sex with non-exisitant fantasy races or something like that.
Half-Humans (that is, any race that bred with humans and had an offspring, that offspring) were sorta typical. The "metahuman" genepool as it were (stealing from ShadowRun where if an Orc and a Human mate you either get an orc or a human, but the genes are compatible) was sorta fantasy standard, don't know why.
Half-dragons on the other hand (paw? claw?) came about due to the Council of Wyrms expansion/setting/books which had a dragon-human cross breed, which would be fairly typical of your gallivanting humans doing debauchery with every race on the (fantasy) plane.
Of course, far far more players wanted to play
half dragons than anything else, resulting in a huge surplus of half dragons where they were supposed to be rare.
Then someone had to try and justify
how such breeding was possible. How? Male dragon uses alter-self (or other polymorphy ability/spell) to become human, and goes off and has fun with some human female, and his spunk ends up so magically spunky that its DNA is unchanged even after the polymorph is cast and expires.
Then someone went, "wait, if it works for humans, why not elves? Or orcs?" and then everything exploded: there were Half-Dragon Dire Badgers and other crazy crosses (the world's largest dungeon has a half-dragon gibbering mouther for gods' sakes--of course, that one wasn't natural, a wizard did it).
And then a 3rd party book came out. The Book of Erotic Fantasy. Which included an entry on what every sentient race thought of sex. Dragons? "I wonder what it would be like to...."