They didn't know whether or not the fleeing suspect was armed.
Maybe it was unwise but the question is whether or not it was legal.
OCGA16-11-126)Anypersonwhoisnotprohibitedbylawfrompossessingahandgunorlonggunmayhaveorcarryonhisorherpersonaweaponorlonggunonhisorherpropertyorinsidehisorherhome,motorvehicle,orplaceofbusinesswithoutavalidweaponscarrylicense.(b)Anypersonwhoisnotprohibitedbylawfrompossessingahandgunorlonggunmayhaveorcarryonhisorherpersonalonggunwithoutavalidweaponscarrylicense,providedthatifthelonggunisloaded,itshallonlybecarriedinanopenandfullyexposedmanner.”
O.C.G.A. 17-4-60 (2010)
17-4-60. Grounds for arrest
A private person may arrest an offender if the offense is committed in his presence or within his immediate knowledge. If the offense is a felony and the offender is escaping or attempting to escape, a private person may arrest him upon reasonable and probable grounds of suspicion.
"fleeing suspect"? Your choice of words doesn't seem to be better than the other side that you like to argue with.
What about this Georgia code?
O.C.G.A. 16-5-21 (2010)
16-5-21. Aggravated assault
(a) A person commits the offense of aggravated assault when he or she assaults:
(1) With intent to murder, to rape, or to rob;
(2) With a deadly weapon or with any object, device, or instrument which, when used offensively against a person, is likely to or actually does result in serious bodily injury; or ..........
If you try to say that they didn't commit "assault" then look at:
O.C.G.A. 16-5-20 (2010)
16-5-20. Simple assault
(a) A person commits the offense of simple assault when he or she either:
(1) Attempts to commit a violent injury to the person of another; or
(2) Commits an act which places another in reasonable apprehension of immediately receiving a violent injury.
If someone were to have a shotgun in their hand and tell me forcefully to stop, I would have a "reasonable apprehension of immediately receiving a violent injury".
You are choosing "fleeing suspect". You are only looking at the legal authority to carry a firearm. The legal authority to carry a firearm isn't the same as legal authority to threaten someone with that firearm. You have quoted the citizen arrest law before. I haven't seen anything that supports a belief that they actually witnessed him commit a felony. If they didn't actually witness him commit a felony, then they have no legal authority to make a citizen's arrest. There have been court cases in which people are charged with false imprisonment because they honestly mistakenly thought they were in the right to hold someone. They don't have to "think" he did. They have to "know" that he did. They can't "think" he "fits the description" of someone who has been involved in burglaries, they have to in the immediate time period witness him commit a felony.
EDIT: (I am not a lawyer, but as I understand it)The citizen's arrest statute has requirements of using only the force necessary to hold the person until police arrive from some court cases, if you read through the annotated Georgia code. McMichael is apparently claiming self-defense, which is a justification defense. The state doesn't have to prove that he didn't act in self defense, he has to prove that he did act in self defense. He will have to prove that he was justified in making a citizens arrest. He will have to prove that a shotgun was necessary force in making that citizens arrest. He will have to prove that Arbery's actions caused the altercation, not his threat with a shotgun. That seems like an awful lot to prove with very little evidence.