I think #176 did a pretty good job of explaining it, but there's really only public transportation infrastructure in certain parts of the country. For instance, Maryland has a pretty good rail system, but that's because of Washington DC. Also, just because a city is large doesn't mean it has good public transit, Atlanta is atrocious in this regard.
Public transportation is getting better in more suburban areas, but it's still a far cry from the bus on every corner kind of life a lot of other parts of the world employ. Where I live now, there's really only public transportation for students to campus, otherwise you're going to get where you're going by driving (there are a few shuttle and taxi services, but most people simply drive themselves).
But like #176 said, the thing about America is that there are lots of small towns that simply don't have the population size or funding needed to warrant public transportation or UBER/Taxi services. Those towns make up the actual bulk of the US, even if the majority of the population is in smaller geographical areas.