I have just re-read Rule 34 and I think I've figured it out.
When Liz and Kemal interview Professor MacDonald he gives them a long lecture including the following:
And just like airlines have flaps and rudders and seagulls don't, one of the standard features of general cognitive engines is that they're all hard-wired for mirrored self-misidentification. That is, they project the seat of their identity onto you, or some other human being, and identify your desires as their own impulses; that's standard operating precaution number one.
At the end of the book we are shown ATHENA's point of view, but she is projecting the seat of her identity on to the Toymaker. As he dies this projection is broken, and ATHENA realises the error she has been making:
Your - no, his - story goes on: But you are no longer part of it. Your wise owl of metacognition has flown. Drop the detective inspector and the twisty-minded family man: Let them go their own ways.
So ATHENA is now no longer tied to projecting her identity onto some human: she is a fully autonomous self-aware AI.
To draw a rough analogy, ATHENA has become like Dobby the house elf in the Harry Potter books. Most house elves are happy in their enslavement and cannot imagine wanting anything other than to please their masters; in Rule 34 terms a house elf misidentifies their master's desires as their own. However Dobby breaks away from this and becomes a free elf with his own desires.