Single ended circuits operate in class A, that includes all regular pre-amp / phase splitter circuits; due to non linearities in the transfer function, these tend to generate even harmonics (ie asymmetric output waveforms), this tendency increasing with signal level.
Push-pull circuits tend to cancel out even harmonics that they create, whether they operate in class A, AB or B.
If you are coming to this from a 'even harmonics = good distortion, odd harmonics = bad distortion' viewpoint, my thinking (with respect) is that it's nonsense; best to ignore it.
Rather, my take is that low order harmonics tend to sound smoother than high order harmonics.
Pleasant sounding distortion tends to be due to low order harmonics being generated before higher order harmonics (as the signal level rises).
You may find the http://www.valvewizard.co.uk/gainstage.html download useful, as indeed that whole site.