Opposition to the use of the word is, imo, moronic, and a reflection of the shambolic state of American education. The word 'lynching' was specifically coined to describe a specific type of execution which was extrajudicial. It was coined around the time of the Revolutionary War, likely when a man by the name of Charles Lynch was performing such extrajudicial executions on people who were suspected British loyalists - mostly white.
Not to deny that the American public education system is shambolic, but the problem with lynching is the connotation it has incurred, not its etymology. The infamous N-word, the one that the Boondocks version of Martin Luther King Jr. rightly called the ugliest word in the English language, comes from the Latin niger, which means black. If I called a black person the slur that starts with N and explained that, if he had paid attention in Latin class, he would have known that I was only calling him black, do you think that black people would crown me King of the Black People a la Peter Griffin? The slur for homosexuals that starts with F can also mean a cigarette or a bundle of sticks.
In this sense, it acted as a sort of ersatz justice system in areas which were still 'wild' and untamed, and I believe the overall estimated 'accuracy' of such trials hovered around 66%. At its best the practice erased the privileges granted by wealth and political connections and acted as a 'mob's veto' on the unbiased ruling of a corrupt judge or of the abuse of pardon powers - to excuse those with power who had behaved in a way which would have seen a normal citizen executed. At its worst, it fueled witch hunts or represented an escalation of factional opprobrium, racial or religious or otherwise, to a deadly pitch.
I can't say that any of this is wrong, but it does not change the fact that people associate lynching with racism because, within memory much more recent than the American Revolution or even the Wild West, lynching was largely a method by which white people terrorized black people and maintained white supremacy. Slavery has been almost co-extensive with civilization throughout history, many non-black people have been enslaved, and black slaves were often sold to white traders after having been enslaved by other black Africans, yet, when most Americans think of slavery, they immediately think of black people picking cotton for white masters. Whether or not the word slavery should make people think of that is irrelevant because it conjures thoughts of racism and oppression still relevant to our society, which, if you ask me, is undesirable.
Yeah, lynchings can be an ugly thing. Yes, lynchings have a complicated history in the US. But lynchings in mafia are also ugly. We often kill the wrong person, persecuting the innocent while the guilty go free. It's an often inaccurate, emotionally charged, and driven by paranoia, or personal animus, or by results which have been tampered with. I loathe the pattern of neutering language in a way which makes it inaccurate. Calling it an 'elimination' is sterile and less accurate. The problem is that any word that accurately reflects what is being done - eliminating someone by mob rule often in the absence of hard facts - will have ugly real-world connotations because any such process will be ugly and prone to historical abuses.
There is no escaping that the flavor is voting someone out is killing them, which inherently has ugly real-world connotations and can bring nasty thoughts to mind, but 'lynch' sprinkles racism on top of murder.
I agree that a better alternative than 'elimination' is wanted, but not that elimination is less accurate, although it is perhaps less precise, using the scientific definitions of accurate and precise. Voting someone out eliminates them from the pool of living players. If whatever word we use to mean, "vote a player out during the day", becomes accepted vernacular, then implications like potentially killing the wrong person, voting based on unverifiable gut feelings, and relying on falsified evidence will transfer to the new word unaccompanied by the racist connotation of 'lynch'.
Using the word lynch is good because it impresses into players' minds both the fact that they are engaging in an inexact process that is easily manipulated by both high emotional tides and nefarious actors.
Players should understand that anyway, no?
At the same time, when you leave the game and go into the real world, the word 'lynch' will be accurately tinged with an aura of unreliability, injustice, doubt, and finality that is far more visceral than any connotations imparted by the dry historical record. You will also understand why lynching happened and why it is historically a tempting process because you would have engaged in a simulacrum of the process yourself. You will remember being absolutely convinced that someone was guilty, gathering up a mob, pushing their lynch, only to sheepishly see the flip and realize how wrong you were.
As enlightening of a classroom exercise as this could be, whatever lesson in herd mentality 'lynch' imparts is outweighed many times over by its potential to instigate thoughts of racist violence, almost like a trauma trigger. Should we start every post in the day thread with Heil Hitler and flavor getting voted out as being put on a train to the gas chamber so that games will double as reminders that we can be susceptible to fascist propaganda?