It very well could lead to a clash. That chance is there whether or not we are prepared for it or not. That is the difference. Disarming will embolden them. Arming will let them know to not start anything. Detterence.
The only way to prevent conflict is to stay completely out of their "zone" and let them dictate everything we do. Unless we do that, we have to manage the risk.
Not being ready does not lessen the threat. If they know we will shoot before they fly off the handle, it might be in their (and our) best interests to keep them from flying off in the first place. How many schoolyard bullies pick on the bad @ss (but generally nice guy) of the campus? The bully might want to do something, but the specter of an ass whoopin, or at least someone willing to give him a go for it might change his mind.
They very well might be getting ready to shoot. But if they know we will shoot back, that might change their minds about pulling the trigger.
The might eye that big stick we are carrying and avoid a fight.