You fail to understand that identity is not a fixed label or a concrete concept. It's a social construct.
Most people, when asked what a black person looks like, will list pretty much what an African American looks like.
To many, we don't look "African". To some, we aren't "black". 'African' is one label that pretty much no-one can deny without looking stupid, but "Black" is one that when accepted by Somalis, sometimes sees backlash from other "Blacks".
Plenty of people are tired of being told that they aren't black by those who are supposed to be their fellow blacks, and so identify as only Somali. That's no less correct or incorrect than identifying as Black. Some Somalis who speak Arabic as a first language or live in the ME might identify as Arab, and that's fine, too. Somalis are a diverse bunch in appearance and self-identity.
Also, we don't have an "Arabic" culture, and I'm sorry to tell you this, but Somali culture has been influenced by Arab (Specifically Yemeni/Omani) culture and vice versa for millennia. We live literally right next to them, it's a given.