Windows machine contains several components and one of them is Docker command line: the docker command that you use for everything-management.
Similarly, there is Docker daemon - A self-sufficient runtime for containers, the core. Docker daemons for Linux Containers and Windows Containers are different, but they listen for connections from the docker client on the same pipe. So one needs to be stopped for other to be started. This is the technical reason that you asked for.
But, you can observe that containers started for ex. in MobyLinuxVM is still running and available for connections when you switch to Windows containers. The only thing here is that you cannot manage them because the Docker daemon for Windows does not know how to manage Linux containers in MobyLinuxVM.
Docker for Windows 18.02 now supports Linux and Windows containers running side-by-side via LCOW, using a single Docker daemon.
Now you can use one docker daemon to manage both worlds, it's just about using the new --platform flag in docker pull.