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.

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.