The video doesn't do a good job of explaining this at all.
Ultimately the reason why adding more roads to a system produces more traffic is more people take cars vs. public transit.
Ultimately the reason why adding more roads to a system produces more traffic is more people take cars vs. public transit.
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.
More precisely, more people take cars vs. not take cars. "Not take cars" can be public transit, human powered transport or even not moving at all.
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.
You're talking about the Downs–Thomson paradox. that's a related, but different, problem.
[1] https://en.wikipedia.org/wiki/Braess%27s_paradox [2] https://en.wikipedia.org/wiki/Downs%E2%80%93Thomson_paradox