1) The US is really big. Seriously. Our population density is 1/3 that of the EUs with a similar (but now smaller) total population. Only Sweden and Latvia are less dense as EU member states. Add to that most of the US is more temperate than most of Europe and therefore we have even more desirable land (Barcelona is north of New York City).
That is to say, we have less need for it. Houston and Phoenix, our 4th and 5th biggest cities, just keep expanding out as opposed to up. This has long term costs, but certainly is cheaper.
1a) Gas is also a lot cheaper in the US than the EU. Two car families are plentiful. So spreading out costs less. And all our infrastructure (outside NYC, DC and maybe Boston/Chicago) is based around cars, not mass transit, so you need a spot to park your cars.
2) Local taxes are (in general) done based on the value of a house. If new houses in less desirable places are cheaper to originally buy, they are often also cheaper to hold. They have fewer established tax costs as well for maintenance of public transit or school because those come later (or not at all). What he's talking about is greenfield on the other side of a legal boundary, so there are different (usually fewer) governments to levy taxes. In the US, you may pay taxes to your city, county, state and the country (a lot of caveats there I'm skipping). If you buy a house outside the city, that's one fewer entity that can tax you.
3) There's a huge anti-urban political component. Literally, there are people who want rural areas to thrive and cities to fail. In some states (see Texas and Arizona, where Houston and Phoenix are), these people control the state.
4) Amazingly, for some reason (possibly holding offshore dollars), it's far more profitable to use the same square footage for luxury condos that sell out right away compared to many smaller cheaper houses/apartments in desirable cities.
5) It's literally been sold to generations of Americans that owing a lawn is a sign of having succeeded. That's where the "white picket fence" comes in. There is a huge market demand for suburbs.