Ok, the tiger is a figure for women's desire in the book.
Sophie allows the tiger into the house because she has not learnt that women's desires should be expressed only in limited,'palatable' forms.
Notice that the tiger 'can't be' any of the men who routinely visit the house - so even though he is male he is a figure for an expression of the women's feelings.
Both mummy and Sophie appear comfortable with the tiger and encourage him as he satisfies his (their) insatiable desire for fulfilment.
His desires though also wreak havoc in the home, leaving it unstable. The woman's work of washing, cooking and cleaning is barely possible in the house when he has finished.
When daddy comes home and sees the destruction there is no sign of the tiger: from his point of view there is clearly a link between the destruction and unrestrained consumption he sees and the women in front of him.
He restores patriarchal order by applying reason to the situation with his 'good idea'.
The mother is old enough to know that a woman gets more security in life by accepting 'little treats' from patriarchs than by demanding all her desires are met.
She accepts the offer of tea and Sophie is now aligned with her mother as they head out for their sausages and chips and ice-cream.
Both women know the secret about the existence of desire. Both keep the gleeful memory of what unrestrained desire feels like.
Both consign desire and the tiger to the past to keep daddy happy. And the tiger is never seen again.
Howzat.
In the transition stage of labour with dd2, I recited this book as a way of keeping calm.