Reddit reviews Vox Graeca: The Pronunciation of Classical Greek

Pffff... you're stepping into the most heated debate of Greek scholarship. Before reading the specialised bibliography I recommend these three articles:

1. McNeal, Richard A. (1975). Hellenist and Erasmian. Glotta, 53(1/2), 81-101.
   
2. Dillon, Matthew. (2001). The Erasmian Pronunciation of Ancient Greek: A New Perspective. The Classical World, 94(4), 323-334. doi:10.2307/4352587
   
3. Vernon Kooy. Thomas Jefferson’s Argument Concerning the Pronunciation of Ancient Greek.
   
   Having read that the four books you MUST consult are:
   
   
4. Anastassios-Fivos Christidis' A History of Ancient Greek
   
5. Geoffrey Horrocks' Greek: A History of the Language and its Speakers
   
6. Devine & Stephen's The Prosody of Greek Speech
   
7. Allen's Vox Graeca

Yes, they do teach it the "wrong" way. Nobody on the planet teaches classical languages the way they were pronounced originally. For three main reasons:

1. You would have to first decide on the "right" way to teach it, i.e. choose a location and era and stick to it. Attic was pronounced differently from Doric or Ionian, or from Hellenistic and Roman-era Greek. Homeric Greek was way different from any of those, to the point where Roman-era Greeks needed vocabulary lists to get through the Iliad. We know this because we found their notes and frustrated classroom etchings. Yet all of these places and eras have contributed to the literary canon of "Ancient Greek" and are taught together as one subject.
   
2. It is a pointless exercise for most applications, because there are no native speakers of the language to converse with.
   
3. Most importantly, these languages have been taught all over Europe for many centuries, and completely independently of linguistic studies. Over time, each place has developed its own peculiar tradition of how to pronounce them. When you learn Latin in Germany, the letters are pronounced as they would be in German. When you learn it in England, it's pronounced mostly like English. In Italy, it's pronounced like Italian. But the Romans spoke quite differently from any of those, including Italians. The same is true for Greek.
   
   A good example from Latin is the name Caesar. It is pronounced (approximately) "See-Zahr" in English, "Tsay-Zahr" in German, and "Che-Sahre" in Italian. But we know the Romans pronounced it more like "Kai-Sar". And one of the reasons we know this is that it's spelled "Kaisar" in Greek - whence also the German word Kaiser for "emperor".
   
   As /u/hircc already commented, the basic information is available on Wikipedia. If you prefer an academic monograph, there is Vox Graeca by W. Sidney Allen.
   
   By the way, the easiest way of convincing yourself that Ancient Greek cannot have been pronounced the modern way is the fact that many words would sound the same, and half of the vowels and diphthongs would be redundant. Seeing as the Ancient Greeks invented the alphabet, specifically by adding vowels to the Phoenician script, it would have been quite singular of them to introduce separate glyphs for the same sound.

This book is the definitive book on Greek pronunciation. (There's also a Latin version if you're interested.)