The common mistake is people swerve and brake, which is a terrible combination - you should accelerate through a sudden manoeuvre, as it maintains control through it, much as you should accelerate through corners in general.
Wunibald Kamm begs to differ. For his circle, it doesn't matter if the additional force that causes the friction to be insufficient is forward or backwards on top of the side force. In critical situations either use your friction for lateral xor longitudinal action, never both at the same time. Brake hard, but then sail through the curve. You want that vector to move along the circle and never leave it. As that is very difficult for an untrained driver, better switch hard between both modes.
True if we all drove unicycles - but in the real world, tyre wear is uneven, brake wear is uneven, loading is uneven, the surface is uneven, and those differential forces are what modern ABS seeks to control.
The key difference between braking and accelerating is that in the former case, independent, potentially differentially worn brakes, apply force unevenly, making the chance of a loss of traction on one or more wheels higher. With acceleration, that force is applied through a differential, meaning it will be far more likely to be appropriately distributed.
If you want to decelerate while swerving it can be done, but it should be done through engine braking - and the tricky bit there is matching revs as you drop the clutch back in, otherwise you have too much retarding force and overcome the coefficient of friction, resulting in a skid.
Easier for those of us who grew up with double de-clutching and no synchromeshes, but when you’re in a critical situation, it’s still an awful lot easier to apply acceleration.
