Al-Fusha, is the official Arabic used in the whole Arab countries. Classic Arabic may be the most understandable way of speaking Arabic between the Arabs.
Why non-Arabic- speaker needs to know classic Arabic? First of all one shall know that classic Arabic is the language of the Quran, Allah has revealed the Holy Quran to his messenger in classic Arabic. Muslims need to learn classic Arabic, because they need to read Qura'n.
If they want to go beyond the meanings and secrets of the Quran, they need to learn classic Arabic also; which we call in Arabic "Al-Fusha". Another field that non-Arabic-speakers greatly need classic Arabic in is formal speeches: diplomats, journalists, reporters, and announcers who use Arabic in their speeches need to speak it in Fusha. People also need to learn Arabic Fusha to understand the Arabic books written in classical Arabic.
Classic Arabic is the official language of the academic studying.
Those who want to learn about Islam in any Arab country need to learn classic Arabic, to understand the terms of Islamic Shria. If you have works in Arab countries and your work nature makes you move from Arab country to another, you greatly need to learn classic Arabic, because it is the mutual language that can be used, and understood easily in the whole Arab world. For a Muslim; Arabic Fusha is considered an identity for him, because it is the language of the Quran, his book, and the language of the people of Al-jannah.