I hear the term most frequently used with relationship to mixed race people who, for instance, the parents divorced and the kid was raised in closer contact with the black parent’s family, and may not look black but identifies with black culture.
Personally, I don’t put much stock in this “meme of self-identification” you’re on about.
The other thing is, you’re much more likely to see terms like this when we’re bloviating about race, gender, sexuality and suchlike here on the Dope than you will in everyday life. As you say, for most people the idea that they “self identify” as a woman or a man would be nonsensical, they imagine that they ARE men or ARE women. But for some people this isn’t true…the question about whether they are male, female, both, neither, or something else entirely is not so obvious.
“Self-identify” is a method of allowing us to bloviate about these issues without having to agree. It is a matter of argument whether Chris is “really” a man or a woman, but it is an objective fact what gender Chris identifies as. Does Chris tell people she’s a woman, or does he tell people he’s a man?
So, you self identify as a non-self identifier? 
That is true. Oh, and sorry about the snark. I was just recently in an argument where someone was trying to tell me I’m not X when I am X, and I got a little carried away.
ISTM that the purpose of the verbal phrase ‘self-identify’ as opposed to the simple verb ‘be’ is to contrast it with a different mode of identification - that by others.
Example: I don’t ‘self-identify’ as a white male. I AM a white male. Nobody ever told me I was a woman or black or chinese.
Politically I’d say I AM a liberal(ish)… except that a sweet old woman from Maryland once told me she thought I was a conservative. In that instance I consider I ‘self-identified’ as liberal.
IOW I ‘self-identify’ as X only when another person perceives that I am other than X, whilst I perceive that I am X. Then ‘self-identify’ is used to clarify.
Does any of that make sense? Let me find out after this beer.
Of course I self-identify. I’d know me anywhere. Yup, it’s me.
It self-identifies as a pale lager, thank you very much. Insensitive cad.
(I think I have a new favorite word. Bloviate. Wonderful! I’ve not come across that one before; thank you for that gift today!)
The problem is that “really” means different things to different people. To me, Vick is “really” a man, no matter what’s under his jeans currently or whether it bears any resemblance to what he was born with. To someone else, Vick is “really” the gender of Vick’s current genitalia, and to a third person, Vick is “really” whatever Vick was born as, no matter what surgery or gender role Vick has chosen for Vickself.
“Self-identify” is at least clear as to who is doing the defining of “really” - Vick.
Don’t impose your meta-identities on me!