Is it right?

Most people say 'an MBA' . Shouldn't it be 'a MBA' as the letter 'M' isn't a vowel?

The letter M, when pronounced as the letter (ex. saying the alphabet) and not as a consonant at the beginning of a word, is said "Em". Acronyms like MBA are said by just saying each letter. Thus "MBA" is pronounced "Em-bee-yay", a word that starts with a vowel, so therefore "an" not "a" is the article that proceeds it.

right, it's the sound or how we read it that determines the use of article. Not the apperance.

I guess this is gradually developed to make pronunciations easy and smooth as time passes. That's the way it goes. That's how languages are.

Well, what happened is that originally the indefinite article was always "an" in Middle English, but then the /n/ at the end started getting dropped, but not before vowel phonemes, simply because that'd require the insertion of a glottal stop (which would eliminate any of the "benefit" of dropping the /n/).

A far more recent thing that is similar to such is the common pronounciation of "of" in American English when it is following another word. At least here, it *usually* gets incorporated into the preceding word as a enclitic which is just /@/, but if there's another word following it which starts with a vowel phoneme, the enclitic is often /@v/ instead, for reasons similar to why "a" alternates with "an".

It seems to me that when I was young, "a" was used before "MBA" in writing, but we'd read it as "an." Now I mostly see "an," which I like, since it makes sense to write it as it's said.