Independently of question of Cygwin vs MinGW, the libvirt project chose to use the LGPLv2+ as its license. While there are interesting debates to be had on whether to use GPL vs LGPL for libraries & the FSF has a good article detailing some of the tradeoffs, the libvirt project has decided that the LGPLv2+ best suits our goals.
Having made that decision, we want the same licensing terms to be applicable across all platforms, whether Linux or Windows - we don't wish to penalize Windows users over Linux users. As such the Windows binaries we provide must be LGPLv2+ licensed in line with Linux binaries we ship, and we also wanted to build the binaries from a Linux host machine. While we could have used WINE + Cygwin, we decided that MinGW suited our needs. We've nothing against Cygwin - both MinGW & Cygwin are great open source projects and we're happy to see them both thrive & co-exist. In the same way that we choose to use GTK rather than QT for some apps, does not mean we have anything against QT, it is just a choice to be made. The important thing is that the choice is for a completely open source toolchain & build host OS (Mingw or Cygwin on Linux), over closed source development platform (VisualStudio on Windows).