Objective-C isn't going anywhere, just like C++ hasn't gone anywhere, nor has C left the building either.
There are 124 public frameworks in the 10.10 sdk, 357 private ones. While a good chunk of these are written in Objective-C, a good deal of them are written in C, or Objective-C with the guts in C++. AVFoundation, for example, is mostly C++ in the "backend".
The amount of effort it would take to move those to Swift would be fairly substantial, and with no real gain. This doesn't mean that new frameworks won't be written in Swift, but still interoperable with Objective-C, this will probably happen - though I doubt it'll happen in my development lifetime. So we are looking at a gradual replacement of frameworks, or superseding with newer ones (QuickTime -> AVFoundation -> ???).
He brings up Carbon, but erroneously as Cocoa actually predates Carbon and Carbon was only meant to serve as a compatibility bridge from OS 9 to OS X. Carbon was meant to die.
I don't plan to switch to Swift unless I absolutely have to. I spend 14 hours a day developing for OS X, but my problem isn't Objective-C, it's the ambiguous documentation and mildly temperamental behavior of certain frameworks coughAVFoundationcough. I didn't need Swift, wasn't looking for Swift. I have nothing against it, I'm sure it's awesome, but language isn't my issue at this point, so I don't really have much to gain by it.