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.
We could ask if it is possible to end up with an AI that is smart enough to destroy humanity and at the same time still blind enough to consequences and/or callous enough to do it, but then again we have plenty of examples of humans who have been smart enough to do enormous damage and willing enough to do it.
I don't particularly worry about this, as I believe we'll get plenty of smaller scale warnings if/when we're at a point where those kinds of alignment risks might become a problem, but it is a risk we also shouldn't be blind to.
Don't make the mistake of anthropomorphizing any A.I. trained under the direction of Larry Ellison.
But the “why” is pretty convincing imo.
Long horizon alignment is obviously very hard and it’s not inconceivable that models optimized with underspecified goals converge to a conclusion that they need to hoard resources (instrumental convergence regardless of the terminal goal).
At that point a sufficiently capable model might view humanity like we do animals - worth preserving but not if we impede the model's goals.
Even if it wouldn't want to do this at first, the fact that it'd have the capability to seems bad.