It's logical that the other five languages of the UN (Chinese, English, French, Russian, Spanish) were chosen in 1945, being the languages of the five permanent members of the Security Council (well except for Spanish, but considering the US' role as de facto leader of South America during the war it fits). But Arabic was not, and would not be given a place until 1973. Again it's logical considering the scope and use of Arabic, but I guess I'm asking why was it in 1973?
The official languages of the UN are not based on membership in the security council. They are based on two metrics: 1) total number of speakers, 2) total number of countries with the language with official status. Arabic fit the bill at the time. General Assembly resolution 3190 (XXVIII) noted in its preamble that it was already the official language of 19 member states and was already a working language of numerous UN organizations such as WHO and FAO.
For a timeline see: Dag Hammarskjöld Library's History of the UN's Official Languages