Why are we supposed to say the “a” as an “e” in “any” and “many”?

This shows the typical pronunciation of any to be /ˈɛni/. The /ɛ/ is the same sound as at the beginning of end, not the sound at the beginning of anvil (/æ/).

Spelling and pronunciation are not strictly related. If you want to pronounce any as /ˈæni/ you're welcome to, it doesn't sound so different that you'll be misunderstood, it's just not the typical pronunciation.

As to why you pronounce it like that. Either you do it deliberately, or it's how you were raised.

Nobody can tell you or any British- American- Canadian- or New Zealand-English speaking person that your pronunciation of any word is incorrect. That goes for all dialects contained within these countries as well.

The reason? English has never been "officially" standardized. Yes, you will find dictionaries and many other books in each country which lay out "accepted" or recommended pronunciation for that region, but none of this guidance is a definitive "rule."

In German, by contrast, there is a prescribed value and linguistic rule for how each vowel, consonant, and thereby, word, is to be produced and pronounced. In truth, no one in Germany should really speak dialect - that's never happened, thank goodness.

This delineation never happened in English, which keeps it something of a happy mess - which it's always been.

According to Wikipedia (which cites Bergs, A., English Historical Linguistics, de Gruyter 2012, p. 495.), the spelling of "many" and "any" are anomalous - for some reason the pronunciation /ˈɛni/ comes from the version of Middle English spoken in southern England, while the spelling is from the English Midlands at the same time, where the words were pronounced differently and spelt with an "a" to match. There doesn't seem to be a particular reason for this. In northern England and Scotland the pronunciation was different again, with the spelling "ony" to match.