Welcome to PCHF.
This is a Motherboard/BIOS thing. Most Motherboards/BIOS will not allow a boot up via a USB device. However, there is work being done to provide flash drive boot up of a striped down version of Windows, but I have not seen anything to support a full blow installation of Windows onto an external drive. From what I've read, the initial steps of the install seem to work, but then you are faced with a
BSOD.
Recommend you install Windows onto your C: (internal) drive and use the external drive for your personal data files.