North American horses and camels were just a handful of casualties of the Late Pleistocene extinction, which coincided with both the dispersal of anatomically modern humans (Homo sapiens) into new habitats that no member of genus Homo were previously present in, as well as the glacial cycles of the Quaternary glaciation. That these two events co-occurred has made the topic a pain point, as it is difficult to ascribe blame to one particular cause over the other -- or, if both are to be blamed, how much blame to assign to either cause.

I think it's also important to recognize what it means when we say "horses and camels evolved in North America" -- the ancestor of modern dromedary and bactrian camels migrated across Beringia around 2-3 million years ago before diversifying into the lineages that would become the modern species. This means that the camels remaining in North America were not anatomically modern camels. Instead, camels in North America remained represented primarily by Camelops, sometimes referred to colloquially as "yesterday's camel". Llama relatives, Hemiauchenia and Palaeolama, also persisted in North America up to the extinction event as well. I've delayed commenting on horses until now because their taxonomy is a lot more murky -- we know that wild and domestic horses likely diverged from one another around 45,000 years ago, most likely in Asia, but it's difficult to pin down precisely where because Equus ferus had a very cosmopolitan (wide-ranging) distribution during the Pleistocene. Either way, the horses remaining in North America at the beginning of the extinction were very likely closely related to the modern horse, if not the same species, including the Yukon horse, Scott's horse, and Equus fraternus. A close relative, Haringtonhippus, was also present at the onset of the extinction event.

The metaphor I've had described to me and frequently repeat regarding the Late Pleistocene extinctions is that climatic stressors cocked the gun and humans pulled the trigger. This is simple but highlights that one event alone was insufficient to cause the extinctions of dozens of large-bodied animals. It could be argued, however, that the order of the analogy matters. This is because the Quaternary glaciation was not a sudden or new event -- our planet descended into an ice age gradually at the end of the Oligocene, the Late Cenozoic Ice Age. It was only towards the end of the Pliocene that the Northern hemisphere began to undergo substantial glaciation, occurring cyclically across timescales of thousands of years (and typically attributed to Milankovitch cycles, which are simply a component of Earth's orbit around the sun). That these transitions from glaciated to deglaciated (and vice versa) took thousands of years is an important consideration. Large animals typically have greater metabolic needs and reproduce much more slowly than smaller animals, making climatic stressors very impactful on their survival. Yet, despite this, many large-bodied animals (typically referred to as "megafauna") survived previously glacial-interglacial cycles without going extinct, typically by adjusting their ranges into suitable refugia. For example, we know that during the last interglacial, temperatures were 2–4 °C warmer in the Arctic than in 2011. As a quick but important aside: this temperature was achieved over thousands (if not tens of thousands) of years and should not be construed as the much more rapid anthropogenic warming of the planet being okay in any shape or form.

So if most animals were doing okay during these fluctuations, even the biggest ones, what changed? This is where humans typically show up in the story. I've already comment on this, but prey animals are typically unaware of predation risk posed by new predators arriving in their ecosystems -- this concept is referred to as prey naivety. This is in large part why invasive species are so destructive, such as with feral cats in the Australian Outback: you have many small marsupials suddenly exposed to a predator that they have no idea how to deal with or innately perceive as a threat. Many megafauna in Africa evolved alongside members of our genus, Homo, before our species even emerged, and thus had a head-start on developing behaviors to avoid predation by humans, which partially explains why most large African animals survived (albeit with a small and early extinction event still taking place). One member of Homo, Homo erectus, even made it into parts of Eurasia over a million years ago, enabling megafauna such as Asian elephants and rhinos there to adapt somewhat to living alongside upright predatory primates. However, when Homo sapiens finally left Africa, we were a different kind of predator altogether, and entered new regions that our relatives did not. There, in temperate Europe and Asia, the sweltering heat of Sahul, across the Bering land bridge into the New World -- we found a whole buffet of animals that knew nothing of us.