It isn't self defense if you are in hot pursuit, you have become the aggressor. Your right to use deadly force ceases when your life (or family and friends) is no longer in danger.
You describe yourself as a libertarian. If you confront a felon who is in possession of your personal property - and attempt re-possession of the property - and said property is a deadly weapon - and the felon struggles to maintain control of the property - why should the felon be given the benefit of the doubt as to intent?
You don't have the right to use deadly force to recover personal property. Do you think that if your neighbor has stolen something from you that you have the right to go into their house and shoot them to recover it?
Does your answer represent the libertarian point of view, conventional legal reality, or what?
Mostly conventional law. In this case though it is in line with my libertarian view. The basic rule is that you can only use deadly force if you are threatened with deadly force. If you go out and become the aggressor (taking the gun from someone) and shoot them, you didn't act in self defense.
I'm open to another point of view. But I don't think we've completely delegated to the government absolute responsibility in the matter of apprehension of criminals who are in the process of conducting a crime.
You cannot use deadly force in the apprehension of a criminal. The cattlemen who rounded up the rustlers and hung them were guilty of murder. But they had every right to apprehend them (including the threat of deadly force) and take them to a legal authority. The downside is that if you are mistaken, then you become guilty of kidnapping, etc.
No, and I didn't frame it that way either. I'm troubled by part of your answer which identify the property owner as the automatic aggressor (and the initiator of force):
It isn't self defense if you are in hot pursuit, you have become the aggressor. Your right to use deadly force ceases when your life (or family and friends) is no longer in danger[...]If you go out and become the aggressor (taking the gun from someone) and shoot them, you didn't act in self defense.
Except the thief is physically contending for physical possession of the owner's deadly weapon. Doesn't that dispute endanger the owner as well?
It seems to me you are implying the owner has a burden to release the weapon into the hands of any thief who grabs it. Shouldn't the thief have the same burden to release the weapon into the hands of the owner without a dispute? We are very clear on who is the thief and who is the owner, after all. As well we are clear on who is carrying the deadly weapon - the thief, not the owner. The rustling analogy does not apply, because the owner is not executing a thief who is already arrested.
Suppose the owner with a deadly weapon in hand attempts to arrest the thief. The thief then disputes the arrest with a deadly weapon. Who is responsible for initiating violence? Who is acting in self defense when they use deadly force?
This discussion is offending the libertarian in me. I don't recall the part where eschewing the initiation of force means open season for thievery and no recourse never...