The right answer to this is Dimitris Almyrantis’, which goes into the motivations and anxieties behind this attitude.
I had passed on answering this, but I’ve just been asked this externally, by a user who pointed out the discrepancy with Chinese and Italian. There are a few linguistic and cultural factors that have made this angry dismissal of reconstructed pronunciation possible.
Greek is in a club of (say) seven “classical” languages, languages with a very longstanding and ongoing literary tradition: Greek, Latin, Persian, Hebrew, Chinese, Sanskrit, Arabic. (YMMV.) Of these, some modern speech communities do not assert an overt linguistic continuity the way Greek now does: Hindi is not Sanskrit, and Italian is not Latin. For that matter, Greek did not always assert its continuity as forcefully: Greeks differentiated between old Hellenic and modern Romeic up until the 19th century.
Some modern speech communities do not have classics from the earliest stages of the language that they venerate in the same ways that Greeks (and, critically, Westerners) venerate theirs, and that they claim privileged access to: the Behistun inscription is not a Thing for Persians, the way the Iliad is for Greeks. Persians have also shifted several scripts in the meantime, and Italians use an orthographic writing system that makes the phonological and morphological shifts obvious.
I think laypeople, when told that scholars think older versions of their language were pronounced differently, still react with some surprise, especially when that older version does not match the current prestige version. Biblical Hebrew was certainly closer to Sephardi than Ashkenazi Modern Hebrew; Middle Chinese is much closer to Cantonese than Mandarin. And of course the reconstruction of Shakespearian English as Canadian Pirate Talk has taken some members of this site by surprise. So the reaction of Greeks is not without parallel.
What exacerbates it is the feelings of resentment that Dimitris already alluded to, and which I’ll restate aphoristically:
- We used to be mighty
- We have these texts as our patrimony
- Those texts are by our ancestors, so we have privileged access to them
- You Franks are now mighty
- You too revere those texts
- You are out to get us and undermine us
- So by telling us you are pronouncing those texts better than us, you are trying to steal our patrimony from us.
It’s a reaction I can see Indians and possibly Arabs also having. Others won’t have that reaction, because they don’t cling as tightly to the old patrimony; or they don’t feel as put upon from the West; or they are more familiar with internal linguistic diversity (so the notion that the texts originally sounded different won’t come as much of a surprise: I surmise the Chinese would have that reaction).