I haven't caught up with the thread, so maybe someone has cleared this up for you. But...
Yeah and let me tell you adding
Person A: "X = Y, but X does not equal Y."
Me: "That doesn't make sense."
You: "Oh we're not systems of formal logic."
The highlighted is where you go wrong.
In math terms:
X represent biological sex such that
X(0) is biologically male and X(1) is Biologically female
Y represents gender such that
Y(0) is Masculine gender and Y(1) is feminine
X=Y is a false statement although moist of the time this appears to be true.
because...
X and Y are strongly correlated, but it's not a 1:1 correlation.
A plot of X will show very high peaks at X(0) and X(1) such that the sum of X(0) and X(1) is very nearly, but not quite 100%, depending on how you plot those with intersex conditions. These are very steep peaks with slopes approaching infinity.
A plot of Y will also show high peaks near Y(0) and Y(1), but these peaks will be broader and flatter. This is because gender (defined by behaviors and expectations) is less polar. The affinity to the poles (Y(0) and Y(1) is weaker. There are feminine males and masculine females. (Also, we are simplifying a complex set of behaviors down to a single variable....)
If you graph X vs Y, you will see a strong correlation, but you will also see significant noise around the 1:1 line.
In short: Sex and gender, when defined as biological morpholigy and behavior patterns, while strongly correlated are not the same thing.
One of the difficulties here is that we are talking about the intersection between a biological trait that can be directly measured, and a psychological trait that can't. If that bothers you, you are likely to have a hard time with psychology/sociology as well. (To be fair, that's one of the reasons I'm a biologist rather than a psychologist.)