Because otherwise she would lose! Why else?
> So I played around some more, and won using
>
> +-3-+ +
> 5 1
> +-7-+ +
> 2 6
> + +-4-+
>
> Why doesn't she break the strategy and play 6 in the diagram below?
>
> +-3-+ +
> 5 1
> + + +
> 2
> +-6-+-4-+
Because you can respond with 7:
> +-3-+ +
> 5 1
> + +-7-+
> 2
> +-6-+-4-+
whereupon every move loses by 0-4 (Catharine's choice at move 6 only
loses by 1-3).
-- Gareth Rees