"Standing" is a particular, legal term of art related to whether a given party can bring an action. Be careful in its use. With that said, I think what you're trying to ask is "on what legal basis may the police require you to surrender a firearm after a self-defense shooting?" If it was merely an "altercation," and no shots were fired, that's a different scenario than if shots were fired, legally speaking.
First, it's a question of state law. Every state has statutes and rules that govern police contact, disarmament, seizure and return of firearms. I don't know what every state's laws say, so I won't try to dissect them here.
Second, some general principles apply. I will point out a couple of those.
In the event of an official police contact, the police can (probably) seize the firearm for a short period to ensure officer safety. This is particularly true if the officer arrives on scene and there's obviously been an altercation, tensions are running high, and drugs or alcohol are involved.
In the event that a shooting has taken place, the police can seize the firearm as (potential) evidence of a crime. Given that a person has been shot, a crime well have occurred, and one of the things the police do is collect evidence . . . like the gun used.
Not necessarily. State law will vary, but there are several ways that property can be "taken." The Fourth Amendment applies to seizures of property and generally requires a warrant, but there are exceptions.