What do the woman, the cat, and the child all have in common?
The woman, the cat, and the child are all acting in self-interest, a state into which they are forced by the modern city. They are all reacting automatically to desires. The speaker is unable to connect emotionally to any of them.
What does “twisting” mean in the poem?
The speaker’s imagination "twists" his perceptions and memories, which both distorts and destroys them.