Let me be clear: I am not concerned with hurting anyone's feelings - I couldn't care less how a subject feels about having a gun pointed at him, so long as I am justified in so doing. What I am concerned with is that I don't shoot someone I don't want to.
I'm also not advocating that we never point guns at people that we do not intend to shoot at that moment. This is a complicated issue, and one that runs into neurological and biological constraints, as discussed below. Let me take it one issue at a time, and then draw them together at the end.
The problem: muzzle discipline is often not practiced
In training, in simulations and in real life, we consistently see muzzles pointed at people (or targets, in training) that we don't intend to shoot at the moment. Sometimes when we see that on the street, it results in someone we don't want to shoot or aren't justified in shooting getting shot or killed.
My focus is muzzling people who don't present an imminent danger to us as we challenge them, and muzzling areas where innocents are likely to be during building entries, searches, active shooter training and so on. We see this when cops challenge an apparently unarmed suspect and they have their guns pointed right at him. We see this when cops are clearing buildings and in active shooter situations: The muzzle is pointed straight ahead into the areas from which people are running or an innocent person might appear (you never know in a building search if you'll find a bad guy, a homeless person, a teenager having a lark, or a resident or an employee). And of course, we see this almost as a normal state of affairs during much target-based training and during simulations.
Years ago at the Smith & Wesson Academy, then under the directorship of now-Chief Bert DuVernay, I was taught what I believed everyone was being taught: that unless you are in the act of shooting someone (or a target), your muzzle stays depressed. I'd modify this to say: Unless you are in the act of shooting someone, or you have justification to shoot them, or you literally can't help yourself because pointing your gun at them is a neurologically hard-wired response. When you are challenging someone or when you are searching and that's not the case, your gun should generally be pointed just in front of the suspect's feet (or where a suspect's feet would be).
This just seems like so much common sense; after all, if you aren't justified in shooting someone, any gun discharge at that point would be negligent. It's so easy to get bumped, to lose your balance or to be startled in dynamically evolving, high-stress situations, particularly those involving movement or multiple people (think of a raid) that this muzzle-lowering precaution seemed not just sensible, but like the only responsible and professional thing to do.
Confusing the issues
When this subject of muzzles comes up, there are three issues that immediately get discussed, and they are often incorrectly commingled. In fact they are separate and need to be analyzed separately.
Legal issues: There are certainly times when you can be legally justified in pointing a gun at someone you don't intend to shoot. But just because you are legally justified doesn't mean it's the right thing to do, and legal justification shouldn't be our only hurdle for so doing. On the flip side, Robinson v. Solano in the 9th U.S. District Court of Appeals, which determined that pointing a gun at someone can constitute excessive force, is often cited as a reason to not point guns at people we aren't shooting. This isn't entirely an accurate interpretation of the case, though, because the facts demonstrate pretty serious misconduct on the part of the offending officer. Plus, this was in the 9th Circuit, an appeals court in which sneezing is pretty much considered excessive force.