If he says you can't, then you're right back at work. More often than not, you will be sent back to work. The running joke is that if you get a sick day, you've got at least one foot in the grave. If you get two sick days in a row, you're dead. Like all jokes, there is some grain of truth in them.
Holidays are a wonderful time to spend with family and friends.
Every military base in the world has at least a small group of people working every day of the year. Myself, while active duty for four years I worked every Christmas and every Thanksgiving. It didn't matter what duty station I was at, out of all of them, my duty rotation fell on these two holidays - just luck of the draw I guess or an elaborate conspiracy. This past Christmas and Thanksgiving was the first one I was able to spend with my family. Another issue when it comes to the military is privacy.