This is according to a statement released by Microsoft Australia (via Polygon), where Microsoft explained the reasoning behind their decision. “The Wireless Controller has been redesigned to allow for higher data transfer speed between the controller and the console. This also required creating a new expansion port design for headsets and future controller add-on devices which is different from a standard audio plug input. […] Xbox plans to develop solutions in the near future to allow consumers to connect many brands of wired gaming headsets to the Wireless Controller for gaming and chat audio.”
As it stands we know that Microsoft is working on an adapter that will allow Xbox 360 wired headsets to be used with the Xbox One, although when will these adapters be made available remains to be seen.