If the collective wonderings of myself and
MarioMeteor
are in any way onto something, the potential for that could well exist.
What we know is that Dedede and Meta Knight were at one point friends circa Kirby's Adventure, and then we've got this gap where they obviously had some sort of falling out, and then Meta Knight tried to overthrow the penguin with a massive overkill battleship in Revenge of Meta Knight.
Since the very title of Revenge of Meta Knight (or, Meta Knight Strikes Back, in Japan) alone makes Meta Knight's intentions abundantly clear, we hold that Dedede probably started it, either inadvertently, or whilst being mindful of some greater issue, or maybe even a bit of both of these things.
MarioMeteor
posited that the Waddle Dee army could well have had a hand in it.
Given Bandana Waddle Dee's position of captain of the guard (we can infer this since he's Dedede's bodyguard), he could well have had something to do with it, too. It wouldn't especially surprise me if Meta Knight doesn't get on fantastically with BWD, as well.
I know they've got a real-world explanation for this, but for the fun of it, I'm going to ignore it and also note that he doesn't get along well with Dedede, either.