Adding road capacity makes other types of trips possible. It's not a simple "hey, I'm taking the bus today because they built a lane". It's more like "Hey, I don't need to worry about uprooting my family or spending 6 hours on the bus to get a job in place X vs Y."
Think about it in computer networking terms. Netflix and Office 365 didn't exist in 1995 because it wasn't possible to make those sorts of solutions work then. Today, we need to worry about network congestion because millions of people are streaming movies.
Very much so. New and bigger roads cause all kinds of associated growth. New businesses and home pop up because it's now practical to get to them in those locations. This increases demand for the roads, so they eventually become congested again. But not just because people like to go from place to place for no reason other than to go.
It would seem then one way to spur economic growth would be to build more roads, transit, etc. Just as building faster internet spurs more internet companies.
This correction might seem pedantic, but I think it is important. One of the lessons of these "paradoxes" (more roads = more congestion) is that one must take into account the whole traffic system.
I'd add that another salient factor is people's housing choices relative to jobs and other destinations -- there is an interplay between road-building and housing construction.
That's in addition to leading people to move further out -- which also intensifies the traffic at the re-entry points to the thinner roads at the center, which are march harder to increase in capacity.
Ultimately the reason why adding more roads to a system produces more traffic is more people take cars vs. public transit.