By tracking who sent what to whom?
And since tracking the devices is actually impossible, how would you know which pager is where and held by whom,
Say one of the pagers wasn't delivered to the person who you "know" it to belong to. Say it got dropped in front of a school. Say another person who has one and even is a Hezbollah member, is visiting a children's hospital, because they're people too and usually have reasons to fight (even if their fighting style is immoral to some). Say another is eating dinner with his family. Etc. Etc. Etc.
There's no way to verify any of that. It's basically just as bad if not worse than carpet-bombing. Unless you implant a device like this on a person and then have surveillance on that person to know where they are and who with when you detonate the device, you're probably doing a war crime.
Dude.
As a third-party to this conversation, I have to say that the dude writing "There is often a gap between common-use language, and the academic function of words (see "racism"). This is why I emphasized the relation of the definitions I provided to the fields of anthropology and sociology, as well as why I stated it is a use almost exclusively found, in my experiences, in academia." seems a tad more credible than the one writing "I'm not superior just because I used a dictionary to quash the logical fallacy of your call to authority."
I seriously think you just missed the nuance he was trying to emphasise, and you started mansplaining something he already implicitly had agreed on. Now you're going for these rather immature "logical fallacy" arguments. Just a tip for that, btw, to up your game in that aspect. Naming fallacies to implicate that the other person is wrong is actually something called "the fallacy fallacy", ie "because their logic contains a fallacy, the conclusion must be false. That in itself is a fallacy. https://en.m.wikipedia.org/wiki/Argument_from_fallacy
So yeah. You're not wrong, but you're also not right in correcting him in any way, and he's not wrong to say that he is right.
I do believe he's an English teacher. Just use your imagination a bit and think of how many of the things your English teacher told you didn't seem to make sense, but when you actually dug into the material, you got an "aaa this is what he meant" - moment.