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"Big words" is a common snarl word used by people too lazy to get a dictionary. Its implication is that anything that can't be described in plain English is not worth talking about y'all, which makes for considerable difficulty for the speaker being challenged when the "big word" is pretty much the only available word to describe what's going on.
Anybody familiar with any kind of jargon - and jargon that leaves outsiders stumped exists even in blue collar jobs - will know that "big words" are just damned useful. Saying "black hole" is just much handier than having to explain "Extremely dense object of matter collapsing into itself with a gravity so high not even light can escape it" every single time you mention it and even subtly getting that explanation wrong for the sake of brevity. Unfortunately, many "big words" are Greco-Roman and "plainspoken folks" have an irrational aversion to Latin.
On the other hand, "big words" can also, if properly misused, be a powerfully distracting form of bullshit, thus making the argument against somewhat understandable if misguided (after all, such apparent populism certainly sounds good to confused audiences, even if it's really a veiled appeal to stupidity). As above, the proper solution is to invest in an appropriate dictionary.