Even though the reasoning for the center placement given by Microsoft, and then further detailed in Danielillo's answer, does in fact make a lot of sense from a UX point of view... it is also interesting, both historically and conspiratorially, to think back to the origin of the Windows menu, and the Start button, from Windows 95.
At the time, it was considered to have been a poor (even laughable) imitation of the Apple menu, from System 6.05 (and prior), which was (and obviously still is), in the top left1.
Now that mobile devices have become much more prevalent - often outnumbering desktop devices in some parts of the world - the bottom centered "Home" button, and its Android equivalent, is now, in some respects, more ubiquitous than the left hand side placing of the Apple menu/Start button in the respective desktop OS.
So, logically (from a Microsoft point of view), it would make sense for Microsoft to imitate this center placing of the "Home" button - of these (relatively) new-comers who have finally achieved market dominance - by now relocating the Start/Windows button to the center of the screen, as well.
It would have been interesting to see what would have happened if Jobs2 had placed the Home button of the first iDevices on the bottom, or top, left corner - which would now seem to be an utterly bizarre placing - in order to replicate the desktop experience. If this top, or bottom, left placing of the Home button had taken hold and gained acceptance, would Microsoft still now be moving the Start/Windows button to the center of the screen..?
Somehow, I don't think so.
Imitation is the greatest form of flattery.
1 Yes, Apple did derive the Apple menu from the Xerox GUI, but that's not the point of this particular Q&A.
2 Maybe Jobs, ahead of his time, had already realised that center placement provided a better UX experience on the iDevice, than a corner placement? No doubt, in the original Human Interface Guidelines (1995) there is an explanation as to why the corner placement was originally chosen.