Comment by Perseids

As I've written above, I've found https://ai-2027.com/ to be a compelling description of how this could happen.

In my words: If AI gets intelligent enough, it will be incredible useful to connect to real world machinery. Think about how much cheaper building houses could be, if all the labor would be close to free. In general, dirt cheap, competent and abundant labor would revolutionize all parts of the economy. People are already trying out near autonomous AI companies today. When AI gets intelligent and cheap enough, no human-led company can compete with AI-led companies. When AI gets competent enough with real world interactions, human blue collar work can't compete. Imagine economic growth not in the single digits, but 80% or 300%. Countries not participating in (reckless) AI growth will quickly be left by the wayside. At this point, we don't even need to allure to military concerns to see how human oversight gets sidelined.

All of this is only ("only") contingent on sufficiently intelligent and cheap AI. If you don't accept this premise, the rest doesn't follow. (There are multiple arguments, why this could be, but that is another discussion.)

If you accept the premise, how would AI 'extinct' humanity? With 99%+ of the economy under AI control, the possibilities are endless. And given its enormous GDP, cheap to accomplish. Probably even for a single AI company in the above scenario. Killer drones? Engineered virus? Poisoned water supply? Let your creativity run wild. You just need an entity that is persistent and well-resourced to reach every last human settlement.

The why is a question about alignment (and out of scope of this comment). As a simple comparison, humans are only mildly aligned with preserving nature. It takes up so much space, protecting it takes an annoying amount of resources, etc.