First, let me kill that idea. Anthropologists do not accept the idea that early humans were cave dwellers. While there have been a few groups of people who did, for the most part, caves are not very hospitable environments. They are dark, cold, and wet. A lot of material was found in caves because neanderthals and early anatomically modern humans used these caves as part of their rituals.
As for how misogynistic early humans were, there is a lot of discourse on this matter. Almost certainly there was a lot of division of labor, but it is complicated to determine how these people lived. We usually look to existing hunter-gatherer societies to give us some insight. I need to look into this study more, but it seems to have some useful information related to this topic.
Ignorance & Headlines
Now as to why the article in question makes the claims that it does. For one, it is a matter of ignorance. We are still clinging to a lot of false myths about early humans. For another, it fits an agenda. For these articles, the truth is less important than getting a lot of readers. The topic resonates with a lot of people and so, even if it does not match scientific theory and evidence, it is still a "good" article in the sense that it gets readers.