At the beginning of the story, the narrator's mother insists on taking a cab, or taxi, to get back home. It is raining heavily, and the daughter wants to go back into the cafe and wait for the rain to stop, and also because she wants another "gorgeous" banana split. The mother, however, is insistent that they take a taxi home straight away.
In the story, Dahl writes that the mother and daughter are "wearing ordinary hats and coats" and that it is "raining quite hard." The implication is thus that the mother wants to take a taxi to get back home simply because she does not want to walk in the rain, especially as neither she nor her daughter seem to be wearing clothes suitable for walking about in the rain. It is also worth noting that neither the mother nor daughter have an umbrella with which to keep the rain off them. This deficiency is, of course, soon remedied by their encounter with an old gentleman who gives them a silk umbrella in exchange for a pound note.
We are also told that the mother and daughter have been to the dentist earlier in the day and that, as they are leaving the cafe, it is "about six o'clock." This implies that the mother might feel as if she has had a long, tiresome day. She is perhaps eager to take a taxi so as to get home as quickly as possible, and, as it were, put her feet up and relax.
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