the infamous moment he walked by Jim Harding on the sideline, said something to him (he was facing away so we don't know exactly what he said), and Harding's response was, "Then f'ing fire me!"
That was about a decade ago now and Harding is still at Utah, but his career did go backwards after that moment and he returned to being only a position coach rather than an OC.
I can believe that Kyle was not intending to fire Ludwig. I can also believe that working for Kyle can be extremely hard at times, and even more so when things aren't going well. My best guess is Ludwig had finally had enough of dealing with the crap from Kyle. He's worked too long in this business to quit mid-season simply because of a 3 game losing streak.
Any way you slice it, though, this is not good for Utah's season. Ludwig was never the flashiest OC out there, but he was very competent. He had proven that at every stop. He's also had lots of practice at Utah making the best out of nothing when invariably the QB situation goes awry. This former Northwestern guy is a big step down on paper.