I believe it's the reaction time lag, not using the brakes instead of the throttle to slow down. Basically people suck at staying in the ideal position half way between the car in front in the car in back. Because of that they brake hard as they come close to the car in front. The next car has to brake harder... till you end up with cars stopping. So it's the human reaction time combined with cars accelerate (generally) slower than they brake.

This. There are lots of studies that have pointed to slow re-starters as the prime culprit for traffic. And it's only gotten worse with cellphones because now there is something to longer distract people when the come to a stop.

Slow-restarters and sudden late-brakers. This is really all about an oscillating wave being carried vs mean flow speed. The best part when you get the hang of it is that in many situations when you can anticipate the "slow-restart/sudden late-brake" of a dozen or so cars before you (and a couple behind you), you can act as a dampener as you strive to keep near the mean flow speed, and delightfully see the phantom jam downright evaporate in your rear view mirror.

I think it's that most drivers just don't pay attention. I'm able to maintain consistent following distances as speeds change if I pay attention to doing that.

The other problem is that if you maintain a gap as traffic speeds are slowing, someone will cut in front of you to gain a car length. Then you have to slow down using the brakes.

Human reaction time is always there, but driving a stickshift generally teaches you to be more observant & plan ahead more- to anticipate and try to avoid extreme braking or acceleration situations.

I drove stick for years, and your parent is right on. And, back in an automatic, I've naturally regressed, I freely admit.