What is the difference between Arabic and Arabian? Why not "He is AN Arabian?" I am a bit confused.
It is normally used in some set phrases like "Arabic numerals," but the official term to describe the nationality is Arab. Some people do use these interchangeably though (although some people may find it to be politically incorrect). Best to stick with Arab as a nationality and Arabic as a language :)
"He is Arabic" is definitely wrong but is used by some English-speaking people unfortunately.
At the very basic level, and as Alex beautifully explained it, an 'Arab' is a person (a noun and an adjective that relates to people/race), while 'Arabic' is a language and can be used as an adjective denoting an affiliation with the language.
So you can say "I am learning Arabic", "I love the Arabic language", "I don't like to watch films with Arabic subtitles", "There are no Arabic signs in this airport", "I have five Arabic textbooks" and so on.
You can also say "He is an Arabic-speaking person" but you cannot say "He is Arabic".