First off, these guys can cut the crap about having no idea why this happened. Maybe they don't know what triggered the response on that specific day, but obviously something petty happened in the past, probably years back, that neither side can let go of.
That's how neighborly feuds work. It's pretty much universal. Each side gripes and bitches about the other quietly, maybe you toss a snide look out of the corner of your eye at them, maybe you give the polite wave and half smile while muttering "asshole" under your breath when you see them back down the drive way, all the while biding your time, it can go on this way for years. Most of the time nothing will ever come of it, a sort of domestic Cold War if you will. Both sides stock piling angst for one another until one party moves or dies. But sometimes, well sometimes things get nuclear and you have to stick a steaming pile of dog poo in your neighbors mailbox. Shit happens.
I learned from the best as far as all this stuff goes. My parents have had a lonnnng standing Cold War feud with one particular neighbor. Pretty sure it started over some disagreement regarding fallen twigs or leaves or something. I can't remember exactly what it was. All I know is the neighbor continues to toss leaves he feels fell from our trees back into our yard and we continue to look out our window and wonder what kind of crazed lunatic goes through such trouble as sorting out leaves and determining their parental genesis. It's fucking nuts. It's passed the point of the friendly wave and silent asshole muttering at this point, but it hasn't gone nuclear as of yet, so at least I still have time to warn them to check for security camera's before dropping off the family dogs poop first class.