What mutual history? (I hope you say anything but religion) Mutual history as a people and ethnicity is with Ethiopians (Oromo's, afars and so on) and Eritreans (and the tutsi few other countries), that make up quite possible the oldest ethnic group in africa, afro-asiatic cushetic people, rather ancient genetic make up that goes back far far. Language wise quite related to few of the above (Oromo's in particular).
Second language being arabic doesnt mean anything more then that, its a 2nd language of throughout culturally influential dominant peoples in nearby region (just a peninsula across, hence close trade and cultural ties since, but that doesnt make a people). Its mainly to strictly because of the religion (and becoming the language of knowledge due to it, like Latin used to be). There are tons of countries that have arabic as 2nd language (several west african countries).
And did I miss something? Country acknowledges itself as what? (I dont hope you mean being member of Arab league, Somalia is called only non arab member for a reason) Honestly, did you learn this in school?