”... it attacks female chromosomes.”
Well, you just failed biology, but I am going to do a little charity, give the benefit of a doubt.
In most mammals, humans included, female is the default unless you add chromosomes. If you go after “female chromosomes”, then all males of the species will have half their DNA shredded as well, thus leaving nobody of either gender.
X X = Female
X Y = Male
X Y Y = Genetically atypical male; Jacob’s Syndrome
X X Y = Genetically atypical male; Klinefelter sydrome
Y Y = Not humanly possible ; won’t make fetus
Human life is impossible without at least one X chromosome!
So let us flip it around and kill off all the males. From the five combinations shown above, one cannot happen, and of the four that do happen, three (those with at least one of each chromosome) result in Males. The Y chromosome can be targeted without wiping out the entire species though; all the males will be gone but the females will still be around.
Well, it’s not terribly hard to fertilize an egg with technology we’ve had for decades. Aside from both the genetic “father” and the resulting child being female, and reproduction requiring outside assistance, humanity could survive. At least those with access to the sort of medical care that only the First World offers, and even then only to those with plenty of money.
At that point, it becomes more of a sociological thing as finances become the determining factor in survival. Would we become a bit more Socialist for the health of our species, or would we be Capitalistic enough to put profit ahead of survival? We’d have a MAJOR social change, and I think it safe to say that the US would actually be hit harder than even the poorest regions of Africa and be the first nation to topple. Maybe humanity would make a united government, maybe we’d become a dystopia, but there is no way the US would survive, which would lead to a power vacuum in the world that would cause even greater upheaval… okay, let’s just stop there and leave it at there being drastic social effects.
In the end, I don’t think losing one gender would kill humanity….. though it may cause humanity to kill itself.