common knowledge will tell you that this is because of a mistranslation/misunderstanding of the first edition Monster Manual, where they somehow turned "smell like wet dogs" into "are dog people"
So, kobolds as we know them today have their roots, like a few of D&D's classic monsters, in Gary Gygax and David Arneson's gaming tables. They first pop up in their Chainmail game as a variant of goblin.
(I'd have to do more research, but, honestly, I get the picture that when a lot of Japanese people talk about playing D&D back in the 80s, they were playing Basic D&D, not AD&D. We know for a fact that Record of Lodoss War, which really shaped a lot of Japanese fantasy for a while, was based on Basic D&D.)
In 1986 or so, AD&D would get its 2nd Edition, which meant more Kobolds! And, in a truly funky case, even though the text-based description would be the same, we'd get two wildly different artistic interpretations.
Kobolds are clearly meant to be reptilian in first edition, so I don't know why they're more ratlike in 2E, but they've been so inconsistent so far that you can't really attach logic to it.
(A bit I forgot to mention about 1E is that they were mentioned as hatching from eggs in that edition, which carried over to 2E as well. Clearly reptilian, right?)
Them speaking draconic in 3E is the first hint of a connection to dragons (though there might've been a 3E splat that explain kobolds have draconic ancestry, I'm pretty sure 4E is the first time that was made explicit.)
they'd also get three whole pages in the 4E Monster Manual! Way to go kobolds! Even if most of that is just giving stats and tactics to various kobold classes...
It's clearly based on the first 2E drawing, but explicitly reptilian like the 1E art.
They'd also get *three whole pages* in the 4E Monste...
a boopable snoot.