Amplifiers can be either symmetrical or asymmetrical. A symmetrical amplifier has both positive and negative power supply rails and the signal rises and falls centered on the 0 volts point exactly in between. An asymmetrical amplifier has only one power supply rail and the signal is biased to a voltage midway between zero volts and the power supply voltage.
In a symmetrical amplifier, any distortions that occur affect both the positive and negative half-cycles equally. This leads to the production of harmonics that are odd-number multiples of the input frequency. For some reason, odd-order distortion sounds exceedingly unpleasant to the ear.
In an asymmetrical amplifier, distortion will affect the positive-going and negative-going half-cycles differently. This leads to the production of harmonics that are predominantly even-number multiples of the input frequency. Oddly enough, the ear likes this sound, as electric guitarists have known since the invention of the instrument.
So, when an amplifier is pushed hard, if it is symmetrical it will sound bad; if it is asymmetrical it will sound pleasant. It is a fact that distortion can sound pleasant, so long as it is even order.
On to something else…
An asymmetrical amplifier must always have a current flowing through its output transistor or other amplifying device. This is called Class A. An symmetrical amplifier can also have a so-called standing current too. This would also be Class A.
It is also possible though that a symmetrical amplifier can operate in Class B where there is only a very small standing current, called the quiescent current. Asymmetrical amplifiers cannot operate in Class B.
So here is where the confusion lies. Class A is not necessarily good in itself – it is the asymmetrical amplifier, sometimes known as single-ended, that produces pleasant even-order distortion when driven hard. A Class A symmetrical amplifier would produce unpleasant odd-order distortion when driven hard.
So if you want to push the preamp hard and create pleasant even-order distortion, you need a Class A single-ended amplifier. Class A in itself isn't enough.