BLUF: We don't have to always be the ones trying to be right.
Here's what I've found...if you have an idea of the general flavor of their argument, you can work with it a lot better. Sometimes they see things differently. Sometimes they think there is something that you need to be doing.Sometimes they just want to take things out on you. I had all three in a D2 DH yesterday. Just let them talk for a bit. Understand that in the first two, they feel they have a legitimate gripe. Don't ignore that. You don't have to talk them out of it, but it'll help the escalation factor if they don't get frustrated by you bottling them up.
1. Great pickoff move to 2B, F4 just doesn't get the tag down in time. I see (home) DC coming out of the 3B dugout towards me, and I can tellthat this isn't an angry conversation (yet.) I get him to blink by simply walking towards him and saying, "What's on your mind, Bob?" This minimizes the confrontation aspect. He says why he thought the runner was out. I let him finish his ten-second explanation, then he asks me what I saw. I give him my seven-second explanation, and that was that. I don't think it would have gone quite as well had it been a battle of who gets to talk over who.
2. Next half inning, home team is starting to pull away. With R2 and a chopper down the 3B line, the play goes to 1B. I move into position in the working area near B, and BR beats the runner by a hair. DC comes out of the 1B dugout, and I can tell that he's pissed at life. I let him vent for about five seconds about how the throw was a full step before the runner, and when he pauses, I tell him that I had the runner beating the throw. He resumes rant, I walk away, and now he knows he has to make a choice. He vents all the way back to the dugout.
3. Next game, I have a visiting batter turn inside on an inside slider that hits him. Had it not, it may have reached the zone, but it didn't. DC comes out (I was confuzzled and could have handled the meeting place better, but that's not really important to this.) He does have a legitimate argument--that it was deliberate and I was taking away the inside corner by letting batters do this. I let him explain his argument. I explain to him that there are two criteria I judge HBPon (using the rulebook and interpretation language,)and both were met. He starts to repeat his argument, and I tell him, "Bob, I understand what you are saying. I get your point." That doesn't mean I agree with him, but that he had his say and it was received. He's not any less mad, but it ends the discussion.
Now, I can't say that these would work with less-experienced coaches--ones that don't know how to argue. Guys that do this for a living have a goal when they come out--and if it's to get tossed, there's nothing I can do with that other than make sure I don't do anything indefensible before, during, and after. On the far more common occasions of coming out to argue something substantive, they aren't generally going to cross a line unless they feel frustrated that they are not being heard.