And I think that most people who ask the question are asking it as a "gotcha" question, and they either deny that "biological classification" has any validity, or they deny that "social construct" has any validity.
But science knows better, as will you, after reading https://en.wikipedia.org/wiki/Klinefelter_syndrome, which says:
“Klinefelter syndrome (KS), also known as 47,XXY, is a syndrome where a male has an additional copy of the X chromosome. The primary features are infertility and small, poorly functioning testicles. Often, symptoms are subtle and subjects do not realize they are affected.”
In Complete Androgen Insensitivity Syndrome affected individuals have XY sex chromosomes but appear female because their body does not respond to naturally occurring male hormones.
Chromosomes themselves aren’t sex, and only some animals’ sexes are “programmed” by their chromosomes. For example, alligator embryos’ (future) sex is determined by their incubation temperature.
People with Klinefelter syndrome are male because they have testicles, underdeveloped as they may be.
Edit: typos
That makes sense to me, but then still the question is unanswered, what is the definition of "woman" in a social context? We have the biological definition, but the other definition is still seemingly ephemeral.
Edit:
Small spelling errors. Also, what makes this a loaded question? I agree it's difficult to answer, but on the surface at least asking for the definition of a word doesn't seem loaded to me.
Biologically, a woman is a human with two X chromosomes. This would be the best scientific answer I would give if someone asked me that question.
Socially, a person can choose to be perceived in any role they wish and which is accepted by those around them -- or not! In other words, social gender roles like other roles are varied around the world and over time. If someone feels more comfortable in a different role, I'm certainly ok with that.
I don't think one is able to change one's biological status but society has accepted that people can live in a different role than their biological status.
* Edit: I should add that I have two trans family members.