My ethnic heritage is a part of who I am. I'm not a nationalist or a separatist but I am pro-Black African unity. I can't imagine going through life not feeling some kind of connection or belonging to a group. You can say 'I'm just human', and I would agree that race, culture, ethnicity etc. are morally irrelevant characteristics, everyone's interests deserve the same equal concern, but the nature of love/empathy is necessarily discriminating. I view African people in the same way that most people view extended family members.
I doubt humans will ever really think of themselves as 'human' until they come across some kind of alien life-form with human like intelligence, or even create artificial intelligence with a human-like consciousness, who we can compare and define ourselves in contrast to (we're not the only sentient beings on the planet but we can't verbally communicate with most non-human animals so our relationships with them are different, they're not relationships between intellectual equals).
It's not surprising that Whites wouldn't identify as 'White' or feel connected to other White people if they were raised/live in a predominately White society that has never been historically subjugated by any non-White groups, no one became 'African' or 'Black' until the slave trade and colonialism of Africans/Africa. If you lived in a predominately Black environment, you would be reminded how unlike the majority you are on a regular basis, you would probably feel some self-consciousness (not necessarily bad) for that reason. When people are in the minority (not just racially/ethnically but even when it comes to hobbies and interests, views etc.), they tend to feel a connection other people who differ from the majority in whatever way they do.