Ah, I see someone has quite the chip on his shoulder. Sorry I can't help you with your complex. To touch on your first part, the Army, Navy and Marine Corps predate and the Department of War by 14 years. I'm not sure what you were trying to prove with that little factoid, but it neither proves nor disproves anything.
However, as you find yourself to be so smugly astute, I'm sure you can piece together a cursory understanding of subordinate command relationships. Do you honestly think that being placed under the Department of the Navy is not equivalent to being a temporary DoD entity? I suppose, by your logic, no one in the Marine Corps is serving in a DOD entity, because they, too, fall under the Department of the Navy? You're being obtuse simply because your feelings are hurt. As was stated earlier, the point of the argument is whether someone was "wrong" in calling the student body at West Point the "United States Corps of Cadets." No one, including me, is truly concerned about where the USCG ties into the fabric of the national defense. The point was, and is, to defend the rightful statement of another forum member--a statement that was challenged by someone whose sense of pride exceeded their knowledge of the actual legal naming convention.
Try not to be so obtuse and quick to anger over some supposed injustice toward your service. Your argumentative style and attempts to sound learned on the nuances of the USCG really only make you sound like a petulant child, claiming his dad can beat up somebody else's dad. Get a grip and try to acquit yourself with a bit more class, as most of us would expect as much from an officer, if you are indeed one.
The Continental Navy was disbanded prior to the creation of the Department of War, and the U.S. Navy was not created until 1798.
Yes, I will say that falling under the direction of the the Department of the Navy is not the same as working directly for the Department of Defense. You of course are welcome to run for Congress, win, propose a bill, and then rewrite the U.S. Code dealing with this subject, if you'd like.
Your "I meant to say DoD entity" comment is nearly the very same comment that caused two very senior officers (both 4-stars) to talk at USSOUTHCOM after the comment, Freudian slip, was uttered in the presence of the most senior enlisted member of the Coast Guard. So if you think this is an unwarranted "chip", this is quite a bit of history there.
Unfortunately, your general ignorance is rampant in the Department of Defense and component services. I will always appreciate the comments from members of the Army, Navy, Marine Corps, and Air Force, especially from junior officers like yourself, that was not based in reality, but in some self-defined reality. The general "I will lecture another service about themselves", while they know very little. At 500,000 strong, I would not expect the Army to know much about other services, especially an O-3, however, I would expect a combatant commander, who's sole existence is joint, to have a little idea of the five services of the military, I don't think that's asking too much.
In the end Tom, you may just want to "stay in your lane" or....do some research, as the average Coast Guard officer will know far more about your service than you know about theirs.