not trying to gatekeep classics here from people having a silly fun time on tumblr. i said people who are interested in the odyssey and that's what i meant, and i'm absolutely including non-academics in this category. i am not a classicist! i've never even been a classics student! i just read (and continue to read) the odyssey for fun.
prooftexting isn't a term that comes from classics, either—in biblical exegesis (bible interpretation), a proof text is a passage the supports an argument for a belief. but prooftexting is the practice of taking an isolated quote as support for a position—extracting it from any context that might not support your agenda. christians are notorious for this (speaking as a practicing christian), even without the vocabulary for it, because once you jettison context and an honest attempt to understand a very, very old and very foreign text, you can make the bible say whatever you want it to.
it's a useful term to be familiar with, i think, because how people (primarily thinking of those in fandom) receive other ancient literature can look very similar. classical reception is (the study of) how "the classics" are received, and encompasses things like "how do people interact in a fandom for a retold myth?" and "how do people post about myths on tumblr?"
a lot of people come by ancient literature secondhand. for example: getting into epic the musical and then being interested in the odyssey. but reading the odyssey in its entirety takes more time and effort than a condensed version; it's not always easy to understand. there's a gap between us and the world of homer, and in trying to cross it, people carry away many different meanings.
this doesn't always jive with a fandomy approach to texts: (many) fans want continuity, authority, accuracy. they want a word of god to back them up. with works from before the concept of intellectual property, without knowable authorial intent, you just don't really get to have that. and what seems less intimidating than trying to read ancient literature? taking your meaning from a snippet or a summary instead, and treating that as the authority. ie, prooftexting.
... and that's basically normal, i think. we can't read all things all the time, and if you're having a fun fandom experience with the epic cycle, who am i to say thee nay? but the result will be, inevitably, further divorced from the source material—and some people having a fun fandom experience do care about that, and want to know more!
anyway, not all prooftexting is equally, idk, disingenuous? if you go hogwild with headcanons about odysseus' sister ctimene, based on the mention of her in one line of the odyssey, it probably doesn't matter. but other times, the departure becomes more blatant, and potentially troubling.
i'll use lies we sing to the sea by sarah underwood as an example, a ya novel that uses melantho, penelope's slave, as a pov character. we know a handful of details about melantho in the odyssey: her father dolius came to ithaca with penelope from sparta; she was raised personally by penelope; she has several brothers; she is sleeping with the suitor eurymachus; she and her brother melanthius are both executed by odysseus and telemachus for siding with the suitors. however, none of the details about her family or history appear in lies we sing to the sea. the author shared that she completed her first draft without reading the odyssey, so i suspect that she simply did not know that we have those details, until after she came up with a different backstory that she preferred. the result is a book in which elements that a reader of the odyssey might consider crucial to melantho's character—her relationship with penelope, her enslavement—are pushed far to the back of its concerns. the melantho of the odyssey isn't really explored, because there's so little interest in the dynamics at play in the odyssey.
and i do think that kind of thing matters. maybe it's not high stakes, but even so, ancient literature is full of serious topics like war and rape and enslavement that ought to be handled with respect. and it's harder to handle them with respect when you lack context. if you pull a paragraph or a name out of context because it helps you argue "this is what's canon"—ignoring that the idea of canon doesn't quite apply to texts like homer—what else are you missing? the text may be saying something else. the text may be saying so much more.
if you lean into your curiosity about what's in ancient literature and what it might mean, beyond supporting your preexisting notions, you're going to have a more rewarding experience as a fan and a reader. that's all.