[p1necone]

I have to assume the answer to that question is marketing. They really want to hammer into you that you're running Linux on Windows.

[thesuperbigfrog]

Agreed. "Linux on Windows" is more clear to me.

The "on Windows" part makes it clear that Windows is the host OS.

Many Microsoft's past products used "for $PLATFORM" in the product name. For example:

Microsoft Word for Windows

Microsoft Word for DOS

Microsoft Word for Mac

It makes it clear that it was the version of the product FOR a given platform.

At first glance "Windows Subsystem for Linux" seems like Microsoft's version of WINE.

Maybe we'll get a real "Windows Subsystem for Linux" when the desktop version of Microsoft Linux arrives.