It's a rule of thumb for "normal" cars.

If anything it takes less power to stop just as fast as you accelerate because of this wonderful thing called the atmosphere.

The problem is that stopping as fast as you accelerate is still too slow to be satisfactory in a lot of cases.

On low end cars that don't have enough power to roast the tires at any speed in any gear you need more braking power than engine power because you need to be able to use 100% of available traction to get from 60-0 for obvious "think of the children" reasons.

Nobody cares if your Yaris doesn't have enough engine to use every available bit of traction to get from 0-60.

Basically "you should be able to brake 30% harder than you accelerate" is a good rule of thumb for economy cars.

When you start talking high horsepower to weight ratios or other vehicular "extremes" rules of thumb don't really work.

I'm not sure if that's what the great parent meant but think about two sports cars on the race track: on every lap at the end of the straights, the better accelerating car will be going faster and therefore need better brakes to slow down to make the next corner.

Braking power is proportional to mass and velocity. Larger mass moving faster needs bigger brakes.

Electric motors can be used to provide some braking via regeneration, but even so braking generally comes down to "how much heat can you dissipate". A small, slow (relatively speaking) city car won't have as much heat to dissipate, so there are more options when braking.