Cascode M6 ensures that the left side of Cc sees a (mostly) constant voltage. Hence Cc current is only dependent on output voltage swing and no current passes Cc due to M10 gate drive waveform.
BTW, I could swear that "Analog Design Essentials" sounds like a sort of book that should explain all of that.
If they say it's obvious, it's probably because the topic has already been
in earlier chapters.