Why say "Hello"?

[Aenlic]

Most etymological dictionaries (if not all;)) don't agree with such a notion, but the concept of wishing the recipient of the greeting "good health" or something equivalent -or inquiring about his health- passed on in English through "salute".
Many languages use similar greetings: salut (French/ Romanian + Catalan toast), ní hǎo (Mandarin), geia (Greek) etc.

The Latin greeting ave is also related to health.

Exactly my point. Ave Maria is translated as Hail, Mary. And yet etymologists insist that hail derives from the Middle English heilen which in turn comes from the Old English hæil, which means - oddly enough - good health!

Clearly, at least to me, hæil and salve/ave all have the same Indo-European root. Yet no mention is given in the etymology of hail or hello of the Latin greeting.