Why Hunt the Largest, Most Dangerous Animals?

Paul Martin's "blitzkrieg" overkill hypothesis requires megafauna to be essentially stupid with no adaptive capabilities to new predators. But when you examine Paleo-Indian lifeways, the evidence doesn't support specialized megafauna hunting. They had very diversified diets - they were hunter-gatherers eating smaller animals, foraging, consuming seafood and fishing. So why would they be choosing the largest, most dangerous animals to hunt when they had such a proliferation of easier prey? The logic doesn't hold. Even the asteroid that killed dinosaurs 65 million years ago didn't kill everything, showing selective extinction patterns require more than just new predator arrival. When you throw an impact event into the mix, it seems to fill gaps that were still unexplained by the human hunting hypothesis. The complexity of megafauna extinction makes more sense as environmental catastrophe than overhunting by peoples with diverse food sources.