I find it absurd, a ridiculous beat about the bush, that was never necessary growing up having friends who were 'black' and that was a fine description just like I'm 'white', what of it, and indeed closer back to (what was then at least) the out of favour/racist/not politically correct 'coloured'.
But as I said, I'm white, so it's not up to me, and if that's really what people prefer then fine - but I have the impression that it's a predominantly American (I mostly only 'hear' it online) turn of phrase, that's spilled over a bit sure, but generally not used/preferred here?
Who is "white" has changed throughout history.
Is Obama black or white?
As a father to a mixed race son, where people draw the line on whether it's "OK" for someone to self-identify or be described as black vs. white is a topic that interests me, and it's wildly inconsistent (but leaning strongly towards it taking far more white ancestry for most people to "accept" that people call themselves white than the reverse), and highly politicised, and there are absolutely no clear lines.
EDIT: I've spoken to my son about answering the inevitable "but where are you really from originally" with "Norway" for example, if he feels safe doing so (and safety is a real concern with that), since I'm Norwegian. It's just as accurate as answering Nigerian (his mother is Nigerian), which would be the answer most people asking that question would be looking for, but would hopefully make at least some people stop to think why they were asking it.
But really these things are not really logical in most cases. Ad es. blacks are blacks, but then you have "asians" who are not "east-asians" nor "south-asians", "latinos" that definitely did not originate from anywhere near the Italian peninsula, "white-irish" as different from "white-british", etc etc. In the inevitable public-authority forms, these days I'm often tempted to just tick "Mixed-other" - I'm whiter than daisies, but in my blood there are probably a dozen different "types of people" who invaded Italy through the centuries (africans, germans, etc etc).
I'm light-skinned enough to be close to ginger, for instance, and this subject has both practical, conversational and occasionally humoristic value when the subject of being outside in the sun comes up. If I'm planning any sort of trip with someone who even has southern European ancestry, not to mention Middle-Eastern or African, it's hardly an unnatural subject to show up in passing.
From that context, it seems incredibly silly that the whole subject just be taboo and remain unmentioned.
Establishing that trust can sometimes take a while, but it tends to help a lot to simply ask about which terms someone prefers etc. if unsure, because just expressing a willingness to adjust tends to be a good sign.
If you mean re 'mixed other', I think the point was just that the categories don't apply well, and 'mixed' is technically true of essentially everyone so eh why not. (I believe 'white - other' is an option though, if that's applicable.)
But it'll depend on background, age, and attitudes, and really the best approach is to just ask people if unsure, as some terms are wildly offensive to one group and not at all to another (prime example of that is that is how "oriental" is deeply offensive to many in the US, while it's not at all uncommon for people to describe themselves as oriental in the UK)
In other contexts it is more precise to say Black because Black people experience a specific form of oppression by being Black, not just non-white. The same is true for other identities (like Indigenous) that are also part of the BIPoC umbrella, of course, but this is why it is often rendered as BIPoC rather than simple PoC.