Khitty > Status Update

3) In humans, sex chromosomes contain the code that sets off a biological cascade that develops the different sex differences (this is the common sex-determination system for mammals; other animals have different means, including temperature or social cues). There are any number of variations (of varying likelihoods) that can occur during this process (ex: activation or deactivation of the SRY gene, different hormone doses, etc.); however, the chromosomes themselves do not define sex in either a biological or medical context. As mentioned before, sex is defined biologically per gamete size and defined medically per genitalia.
4) In the overwhelming majority of situations, humans determine the gender of others without access to knowledge of another's genitalia, gamete size, or chromosomes. Thus, this determination of gender cannot be based on the biological or medical definitions of sex, nor chromosomes. Instead, humans determine another's gender through a combination of gender presentation, secondary-sex characteristics, and stated identification. Failure to correctly identify a gender occurs when these three means are ambiguous or contradictory.
5) A social construct essentially refers to a wibbly-wobbly concept that is defined by a collection of traits, mostly based on their usefulness to humans. These social constructs commonly are revealed when they fall apart when dealing with edge cases. For example, take the concept vegetable, a word with a culinary definition but not a botanical one: off the top of your head, you probably came up with a definition like 'a plant that you eat'. This is incorrect, because (e.g.) mushrooms aren't plants and apples aren't vegetables. Yet, you still have a useful concept of 'vegetable' in your head with plenty of examples of things that are and are not vegetables, even if you can't come up with an discrete definition that can proscribe whether an unknown object is a vegetable or not. Instead, you have a wibbly-wobbly suggestion based on comparison to known objects in that category.
6) Gender is a social construct in a similar manner. (To reiterate: the definition that you may come up with - 'a person with this type of genitalia and with these chromosomes' - is wrong because you do not have access to the information that you are using to define it.) Thus, instead of trying to winnow an exacting definition based on gut feelings, work from how the concept is/is going to be used.
7) Lastly, so I can get off this tangent: separating the many elements of human sex (genitalia, hormone levels, sex chromosomes, genitalia, secondary-sex characteristics, gender identity) is more accurate and more truthful than forcing a binary. It allows space for variety instead of collapsing everything into is/is not. This is especially true when it comes to medicine - a sex-specific disease may derive from any of the different elements of human sex, so determining the etiology (does it originate on the Y-chromosome, or from a hormone interaction, or from lifestyle choices?) improves healthcare for patients and helps focus treatment and/or cures.
(8) Also - if you wouldn't blink at a list of "Fave Female Robots in Fiction", then you acknowledge that 'female' is normally used to mean the gendered social category and not in reference to morph that matches biological definition of sex; so yes, your 'adult female human' definition does, in fact, include trans women.)
Okay. Rant over.