Why should sandcrabs get a paid holiday for a funeral??? I doubt the military will stand down.
It's customary to do this as a sign of respect - it's a display of "public mourning" in the US because a former POTUS has died. :shrug:
You don't personally have to participate, and I won't have a day off at the place that I work. However, the head of each Federal Agency reports to the POTUS. (His Cabinet) GHW Bush is a former POTUS, therefore, this "National Day of Mourning" is being proclaimed in a tribute to him.