What are the differences between the terms "Arab," "Arabian," and "Arabic?"
For example, why do we say "Arabic language" instead of "Arab language?"
"Arab" is either a noun meaning a person from near the Arabian peninsula, or an adjective for things relating to those people.
"Arabian" is an adjective for things relating to the Arabian peninsula.
"Arabic" is a noun referring to the language spoken by Arabs, or an adjective for things relating to that language or Arab culture.
The "-ic" suffix is a common way in English to turn a word (Arab or ecstacy) into an adjective (Arabic or ecstatic). That is why "Arabic language" is used instead of "Arab language" – because the language is of the Arabs.
English is not consistent when forming adjectives related to race, ethnicity, nationality, and language.
He is a German. He speaks the German language.
He is a Russian. He speaks the Russian language.
He is French. He is a Frenchman. He speaks the French language.
compare to:
He is an Arab. He speaks the Arabic language.
He is a Slav. He speaks many of the Slavic languages.
(Slav is a composite ethnicity that includes many nationalities in Eastern and Central Europe)