There would be many ex-Marines here who would disagree with you.
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And they would be legally wrong. They are veterans of one of the greatest military branches in history and rightfully should be proud of that for the rest of their lives. But a veteran of any one of the military branches who is separated by discharge is no longer a member of that branch. No military ID card. No right to walk onto a base. No right to give to receive orders.
It is exactly the same for veterans of the Marine Corps, Army, Air Force, Navy, and Coast Guard.
And they would be legally wrong.
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Legally or illegally, the Marines have something no other service has. Every Marine is a Rifleman. There are no dead-heads in the Corps.
As an ex-Army soldier, I don't refer to myself as a soldier, just a Veteran.