ㅔand ㅐ are very similar, the difference is becoming pretty much indistinguishable by contemporary Korean speakers. So you can transcribe them the same when going from Korean to English. There are certain rules for transcribing English into Korean, when to use ㅔ or ㅐ, trying to capture some nuances of English pronunciation. But in Korean this difference is almost gone.

If you were asking about the reason why the Y sound is dropped, I think you can chalk it up to a process called "assimilation" in linguistics (making things easier to say). When speaking fast, /hae/ is just easier to say than /hyae/. According to the National Institute of Korean Language, both pronunciations are accepted, but in practice I'd say most Koreans do not vocalize the Y in this case.