I referred to my wrong answer in Nick Nicholas’ answer to What is it like to be able to fluently speak Klingon?. The oddity is also commented on in Pedro Alvarez’s answer to What English word is pronounced the most differently from the way it is spelled?
Here’s the deal, from the appendix to Vox Graeca
Greek had a diphthong ει. It was a diphthong in Homeric Greek, /ei/, but by Attic it was /eː/, and had merged with what was in Homeric Greek /e.e/, εε. By Roman times, it was pretty much /i/, and it is transliterated into Latin as <i>. So Εἰρήνη Irene, εἰδύλλιον idyll, συμπάθεια sympathia > sympathy.
Because most Greek loans came into English via Latin—or were spelled as if they did—we rarely get a Greek word in English spelled with an <ei>.
But there are exceptions. Such as deixis and seismic.
So. How to pronounce those?
If you pronounced ει in your Greek like Modern Greek, or even like the Romans did, you would be pronouncing it as an /i/. It would end up [sɪzmɪk, dɪksɪs].
That’s not what happened. Greek was being taught in England with Erasmian pronunciation: an attempt to approach the original pronunciation. Because Greek spelling is conservative, that would end up as a diphthong. And the diphthong that ει looks like (and indeed was in Homeric times) was /ei/.
That’s fine. English has an /ei/ diphthong, so that won’t be a problem. We can just tell people to say δεῖξις as in “day-xis”, σεισμικός as in “say-smi-koss”.
So what happened?
Well what happened is that the [eɪ] pronunciation of long a in English is recent. Like, 18th century recent. Which is why in Scots long a still has its older pronunciation of /eː/.
So if you’re teaching Ancient Greek in England in the 17th century, you have a problem. You know that ει sounds like [eɪ], but if you’re teaching it in 17th century English, there is no English sound corresponding to [eɪ]! Certainly not long a.
So they did the next best thing. (For some bizarre notion of “next best”.) They picked the nearest diphthong available in the English of the time.
They picked long i.
And when English did pick up the [eɪ] sound, it was too late. The teaching of Greek in England was stuck on [aɪ] as the pronunciation of ει. And when Greek words were borrowed afresh into English, with the <ei> spelling, they took the 17th century teaching pronunciation with them. σεισμικός was taught as [saismikos], so seismic was pronounced as [saɪzmɪk].
Language. You can’t make this shit up.