When I was young, a Catholic priest with a thick Irish accent once scolded me and exclaimed… YOU MIGHT NOT UNDERSTAND LATIN, BUT THE DEVIL DOES! That freaked me out a little as a kid, but it's a funny incident to look back upon.
>humans spoke an ancient language that all humans spoke and which all human languages came from.
Maybe Latin is closely related to that proto language? Thinking of The Fifth Element movie now, where the Leeloo character shows up speaking some divine language that only the old priest can partially translate.
as someone not particularly religious, i cant speak much on logic concerning the bible, but to me it would seem more likely for demons to speak their own language. perhaps they latched onto latin for communication with worshippers? i suppose it depends what you believe in