I can have an educated guess from just a brief glance -- especially if the other person doesn't actively tries to mislead me on such an important issue.

And why the fuck do you care about other people's chromosomes?

I don't care directly about chromosomes, they are put an extremely good proxy for one's reproductive abilities, hence an extremely good biological correlate for sex (i.e. reproductive role).

I care about fertility, because reproduction is more-or-less the single most important duty every human has. It is also difficult a space to navigage, therefore all indicators and heuristics that help me appreciate his/her sex efficiently, makes navigating this difficult space much easier, hence is a friendly gesture.

Here is an interesting question for you to ponder: Why do basic facts about human biology upset you so much, so much so in fact, that you use the act of procreation as an expletive?