You two forgot probably the biggest reason why Europe colonized America: We had Rome.
Rome, not the Black Death, was the reason Euros won. Greece thought of modern Math, Geometry, Literature, Art, Theatre, Construction, among other things. However, they were the weak city states, and while Alexander made a brief empire, it was not to last (Except for making Greece a little more unified, and adding Macedonia into it). Enter Rome, a city built on the seven hills. They were an extremely lucky city, there was a powerful, unified empire to the north, and colonies of technologically advanced people to the south. They prevailed over both, but the Greek colonies to the south were very important. The Romans fell in love with the Hellenistic culture (Except for their language, which is why Greek has little to no relatives

)
They then spread the ideas of the Hellenistic culture throughout England, France, Iberia, and Northern Africa, assimilating them and creating the modern Franks, English, Spanish, etc. This shaved off hundreds of years of technological development needed, as the Greek's technological advancement spread throughout the land. Barbarians destroyed the unified empire, creating nation states, halting technological development, and the modern social classes. For the good or worse is an individual case.
In fact, America was developing their own variation of this. The Mayans were the technological but disunified empire, while the Aztecs were the militaristic empire. In fact, Aztecs had some horrible things done to them (Like the fact they aren't from Mexico, they were far northern up. They were forced from their homelands by a different tribe. And once they built their city on the swamp, they were the underdogs, but like the Romans, they prevailed.). Heck, the Incas were pretty much Grome, they had the technology of Greece with the empire of Rome. Both Aztecs and Incas had a great chance against the Euros. In fact, it was a bad sequence of unfortunate events that destroyed them. If it the Aztecs didn't treat Cortez like a god, and the Incas didn't just have a horrible civil war, both would had easily repelled the few Conquistadors.