Short summary:
Why did Europeans invade everywhere and kill everyone?
Because they had guns, germs and steel.
Why did they have those?
Because they were farmers (ie large food surplus, larger population that includes people who don't need to feed themselves and thus have time to invent crafts, weapons, writing etc). Domesticated animals also act like germ vectors, bringing lots of new and nasty diseases to the humans who can't escape as they (higher population densities) are crowded close to each other. Over time, farmers build some immunity against them - hunter-gatherers they encounter didn't.
Why didn't everyone become a farmer then?
Not all plants are equal, and not every place had the same plants. It doesn't make any sense to grow crops with a low calory return when you could be getting a full belly hunting and gathering. That can be solved when you use both local domesticated plants and crops that have been domesticated elsewhere but that also happen to grow at home - but for that you need another place close by with similar climatic / soil conditions, which happened in Eurasia more than anywhere else.
There are also more domesticable animals in Eurasia than elsewhere - partly dumb luck (Africa has loads of big mammals, but none of them is suitable for domestication) and partly because Eurasian wild animals evolved together with humans and got better at escaping us as and when we became better hunters. Other continents were colonised by modern humans with full hunting skills - to find animals that didn't have a chance to evolve better defenses against humans and thus got exterminated quickly. And domesticated animals aren't just a source of clothes, milk, eggs and protein - big mammals help plow the earth and make farming a much more efficient business.
...but lots of other societies had farming too, why Europe?
Most of the other farming societies were isolated from each other. While they did get to develop an "idle" category of society who invented, inventions didn't get around as quickly and efficiently than they did in Eurasia (good commercial routes at constant latitudes with no big deserts in the middle), and coming up with everything ex nihilo takes longer.
Why not other Eurasian societies, then?
The Middle East got over-farmed and can't produce that much food any more.
China was unified sooner than other cultural groups, thanks to well-situated rivers that facilitated communication and to the absence of a power of similar strength to keep it from swallowing everything else. So the one central decision to isolate themselves went unchallenged.
=> as irrational as individual humans can be, as a species we are perfectly rational and each society makes the best survival choices given the environment they find themselves in.
It sounds simplistic and there's nothing revolutionary in there, but it did make for great feel-good Xmas reading. Great examples and arguments from many different fields too.
Also, I felt justified in not liking animals (the idea of petting them or living with them disgusts me, even though I know there is nothing objectively wrong with it). Animal-spread germs were however the single thing most likely to kill my ancestors, and while they probably only survived due to a lucky genetic predisposition, the reflex not to touch animals except to get what is needed out of them may have played some part in it, so it is not as irrational as it might seem in this day and age when pets are most likely germ-free.
