Why doesn't America have a nation-wide railway system like most European countries?

It does already have a large freight network.

But regarding passengers, it can't do so because there isn't enough population density. Most of the population in the US is concentrated near the coasts, so it's not as cost effective.

Also, due to incredibly cheap oil and the growth of the American suburban culture that grew developed after WW2, American's developed their road network more than their rail network.

Everyone wanted to own a larger suburban home and live in less dense areas. This means that everyone needs to own a car. And once everyone is driving, the focus on infrastructure is on roads.