What are some of the ways in which modern culture is “fatalistic” (in the ancient Greek sense of the word)?
This is an interesting question. Perhaps the best way to start is by looking at a Greek understanding of fate. When we do this, a Greek understanding of fate is not consistent. Even in the same author the definition of fate seems to change. With that said, if we had to define fate, then a functional definition can be: fate is what a higher power wills. What is de-emphasized is human actions, to a certain degree.
In view of this functional definition, we can say modern culture can be seen as fatalistic in a few ways. First, there always are wars. Human history can be seen as a history of wars, no matter how much people talk about peace. In light of this, wars may be said to be fated. From a broader perspective, we can say that human suffering also appears to be fated. Second, we can also say that some sort of natural disaster also appears to be fated, as they always occur as well.