Actually, I've heard before that while Miyamoto was working on the original version of Yoshi's Island, he got called to Yamauchi's office, and was asked something to the effect of "Hey, look at this game, Donkey Kong Country. It looks amazing. All the play testers say it's the most amazing thing they've ever seen. You're supposed to be the real big shot around here. Why don't your games ever look as good as this one does? Scrap that weak game you're working on and make something that's at least comparable to this one."
And AFAIK, he had even worked closely with Rare (in both his capacity as Nintendo's "third-party tech support representative", and as the guy who created the Donkey Kong franchise that Rare was borrowing at the time) to make sure that they had gotten the gameplay as dead-on as they could.
When he went back to his workspace, he tossed out everything he and his team had built for the original Yoshi's Island, and started work from scratch on the Yoshi's Island that we all know and love, and he deliberately went in the complete opposite direction with the cartoony pre-cel-shading look, as a kind of "F-you" to anyone who would complain that his games weren't realistic enough.
So I think it's basically that he had a bad experience once involving Donkey Kong Country, and he's a "gameplay over graphics" kind of guy anyways, so he doesn't much care for DKC, or it's role as a "landmark game" in graphics history.
(Although to be fair, Miyamoto's apparently done that "upend the table" thing on some of his subordinates when he's not happy with a product, and he wants to get them all fired up and motivated to do better, so I don't think he can really complain that it's happened to him, but... we really don't know to what level he's annoyed at DKC, or if maybe he got over those feelings years ago... or even if he's still mad, I'm sure he's allowed to get at least two or three sentences worth of complaining in before we can really start calling him a lazy jealous whiner.)