Short answer: Drag on the contact patch of a rolling tire causes the centroid of pressure to be behind the centroid of the contact patch. This displacement functions as an adder to the geometric trail. That's pneumatic trail. It's more with a softer tire and I think with a wider tire.

I think there's something else that affects twitchiness: harder tires have less contact area, so there is less scrubbing friction impeding the rotation of the fork assembly as forces are applied to the handlebar, and in other ways.