half of them died of diseases brought by the spanish...
im not exactly sure what this means, but if you are interested you should read Guns, Germs, and Steel by Jared Diamond.
the reason it happened this way is because the Americas had very few domesticated animals and we get most of our diseases from animals.
That book has some many errors in it I actually suggest you don't read it.
"why were Eurasians able to so easily take over the Americas" than this book.
First there were just more old world diseases which could infect humans than new world diseases. Prior to contact, the old world had about 80 to 90% of the world's total population, so a priori if a disease was to emerge in humans it was overwhelmingly more likely to emerge there. On top of that the old world saw much more domestication of livestock (and particularly livestock animals that had evolved alongside great apes) which in turn created more opportunities per capita for diseases to jump to humans.
For the exchange itself, Europeans were building the ships and sailing them to the New World. It was primarily Europeans on those ships, and especially those passengers who would be most likely to be incubating diseases (the old, young, and infirm) were overwhelmingly more likely to be Europeans headed west. Europeans afflicted with diseases after they reached the Americas would generally not have been allowed on ships back to Europe, or if they were they would likely not survive the voyage. Syphilis likely came from the new world, and it's easy to see how, but if there had been some American equivalent to small-pox it would simply have not been able to make the journey before going extinct as the native populations harboring it were wiped out by Old World diseases.
For it to have been "the other way around" the Americas would have needed a vastly different ecology and the people living there would have needed to beat the Old World to the level of technological development necessary to make contact.
https://www.theguardian.com/world/2018/jan/16/mexico-500-yea...
Within five years as many as 15 million people – an estimated 80% of the population – were wiped out in an epidemic the locals named “cocoliztli”. The word means pestilence in the Aztec Nahuatl language.