It has a lot to do with giving the wrong impression and out of respect for those who are/were part of those units.
While you do not intend it to be, It could be seen as claiming to be part if something you are not/weren't. This sort of thing is kind of a big deal to our military members. Understandably so, as they put their lives on the lien for us. So pride and honor to their signatures kind of matters.