After covering up the exposed weapon, were I a private citizen, legally armed (not LE) I might respond to this hypothetical with something like:
"I am sorry for the loss of your son. I can only imagine how painful that must be. I can understand why you would hate guns. If the sight of my gun was upsetting to you, I apologize. However, I can assure you that I am legally authorized to be armed and am law abiding."
Acknowledging (not agreeing with) his emotion-based view may help de-escalate things. The above statement deflects his aggressive verbal challenge and would probably be something unexpected.
And, simply stating that you are legally armed and law abiding offers a simple, matter of fact, unemotional, and truthful "reality check".
I wouldn't go into my justification for being armed. It's not his business and I have no duty to explain myself to him. Don't let him put you on the defensive about being armed, if you are within your legal rights. Don't say anything that could be construed as impersonating LE. Assume everything you say could wind up in a police report at this point.
The person in the hypothetical is driven by powerful emotions which cloud judgment and make listening to reason next to impossible. Here we have a presumably unarmed man challenging an armed man. Clearly, not rational behavior. Rationality (and the ability to respond to reason) won't return to him until his emotional levels lower. The above statement is geared to lowering those emotions.
The ball is now in his court. He will either escalate or de-escalate.
If he escalates (verbally), I might respond with silence. Silence makes all of us uncomfortable. He may grow frustrated and walk away.
If that fails to work, I might say something like, "You have come over to my table. I did not invite you. I've listened to your concerns and acknowledged your point of view. I don't wish to discuss this further. Please leave me alone. I am in the middle of dinner. "
If that fails to work, then get up and ask the manager to call the police (but keep a visual on the man).
Why bring in the police? Your suggestion of it may make him go away. If not, you want the police to respond and deal with his behavior, which is disturbing the peace.
Importantly, if the police do get involved, it's best if their involvement was at your request. That way, in the report, you are listed as the "person reporting", which is better than being listed as the "suspect".
This hypothetical conversation could develop into a confrontation. Since you are armed, by definition it would be an armed confrontation. You want to do everything to convey to all that YOU are trying to de-escalate.
And you want people around you to see you as trying to de-escalate. Those people are called witnesses...and you want their statements to police (if it all goes to hell and turns into a physical altercation) to paint a picture of a law abiding, responsible citizen trying to de-escalate a situation he did not initiate.
So, to sum up, I would attempt to use verbal tactics to de-escalate. If that failed, I would request that police respond to keep the peace.
