This is mainly due to the influence of the Koran. Educated Muslims were always expected to understand the Koran in its original language. However -- colloquial Arabic actually has changed greatly since medieval days, to the point that an Arabic speaker from, say, Morocco, might have difficulty understanding street conversations in Lebanon or Saudi Arabia. It's possible for people to have conversations in formal Arabic ("fosha") but it's a little unusual.

Other cultures with classical languages that are still readily understandable by educated peoples would include Chinese and Jewish. Until the 19th century Latin was broadly understood by educated Europeans.