Just to add to the other answers here. It’s not actually in the interest of a pathogen to kill its hosts - at least not usually, with a few rare exceptions where the host dies as part of a complex parasite cycle. The healthier its host, the longer it can survive also the more other hosts it can infect. The disease adapts to its host to become less deadly. At the same time of course through selection, the disease by culling those that are particularly vulnerable to it long term leads to evolution of humans who are resistant to it. Eventually the disease and host may even become symbiotes, dependent on each other to survive.

Indeed some parasitic wasps (the Braconidae and the Ichneumonidae) have taken this even further. They actually include coding for viruses in their own genome (the Polydnaviridae). Their own DNA creates viruses which replicate inside hosts to prevent the hosts from encapsulating the wasp’s eggs. (See Evolutionary History of Terrestrial Pathogens and Endoparasites as Revealed in Fossils and Subfossils )

So the most dangerous diseases are ones that have only transitioned to humans recently. That’s why HIV and bird flu are both so deadly. But if a disease is deadly, and their hosts die quickly, then it can’t spread so easily. To spread easily it needs at least some of the population to be resistant, to be carriers. Which then leaves open the possibility that some may be able to carry it indefinitely with no harm to them.

So that’s the basic theory behind the research suggesting that e.g. 96% of the population will die, still you get 4% of survivors. That’s what you would expect, that a few survive. Because if not, it’s not going to be able to spread so quickly. If it has 100% mortality and it gets transmitted quickly, then soon most of the original population is dying. And then especially with intelligent creatures like humans, we are going to notice and start putting quarantine precautions in place, as well as researching to find out how to prevent the disease or cure it.

Diseases can make populations extinct. But normally only if the populations are already vulnerable for some other reasons. E.g. rare endangered frogs pushed over the edge by a disease that kills all of the remaining population.

So, no, this is not a likely scenario. Humans remain amongst the list of species least in danger of extinction, and live on every continent and most of the larger inhabitable islands, and there are also still a fair number of isolated populations of humans with little contact with anyone else, and a few that have no contact at all, to this day the “uncontacted tribes”. So it is not likely that a pathogen could make us extinct.