It’s a unique confluence of incredible capability with little understanding of the consequences of using it. Nobody 100 years ago had the slightest clue that the industrialisation at the time could cause global warming, for example.
As for examples of pivotal moments, WW2 is a good example. We came very close to the world being completely dominated by Orwell style authoritarian one party states. A boot stamping on a human face, forever. It might even still happen. With social engineering and modern surveillance technology as used in China, we could end up in a super-stable oppressive regime with no way out.
Nuclear annihilation is another example. We came scarily close several times as you pointed out.
Global warming is a huge issue, it may even be too late to stop massive changes in our environment that will last thousands of years and shape human history and global biology permanently.
Genetic engineering could change who and what we are as a species in ways that might be hard or impossible to undo. It’s not any one of these that create the hinge either though, it’s all of them happening together.