You could make a good argument that aurochs went extinct due to "predatjon" before the modern era. Humans and other large predators like wolves heavily depended on them for food, and as the climate changed and predator populations boomed, macrofauna couldn't reproduce fast enough to survive. Humans got ahead of the crisis by domesticating oxen right as the last herds disappeared

It's really hard to categorize "why" and "how" a species went extinct if we don't have direct observation, so we really only have that kind of understanding of much more modern extinctions. Even for the dinosaurs, we know a) a space rock of some kind hit. B) the climate changed drastically overnight, and we can measure the effect on plants and the atmosphere. And c) the dinosaurs mostly died off. While we can theorize and use good techniques to analyze the evidence we have, we simply cannot know if the last brontosaurus was eaten to death or starved