This isn't categorically true either, the real world is delightfully complicated, far more so than you imagine. The way cars interact within a road, as they enter an exit the road, or how they choose their route can all create conditions where adding a lane only makes traffic worse and can reduce both speed and volume during peak traffic hours.

I'm really bothered by the mindset of the people against this. People act like induced demand is evil.

In reality, if more people were able to go wherever they wanted to go, that's actually a good thing regardless of if the existing people didn't get to go somewhere faster.

Locally. Under many circumstances. But always? That's not a universal law, as it's a part of a larger system that may perform more poorly if this leg provides more traffic.

Check out the Downs-Thomson paradox.