In the story "The Open Window," why is Framton scared of dogs?

Framton Nuttel is not scared of dogs--at least not of little brown spaniels. Vera makes up a story involving dogs in order to explain why their guest suddenly panicked and went running out of the house just as the three hunters were returning toward the open window with their family dog. When she told Framton the totally concocted story about these same three hunters and their dog being killed three years earlier when they were all sucked into a bog while hunting on the moor, she had provided several identifying details by which Framton would recognize them as the same men and the dog who were supposed to have been killed.

"Poor aunt always thinks that they will come back someday, they and the little brown spaniel that was lost with them, and walk in at that window just as they used to do. That is why the window is kept open every evening till it is quite dusk. Poor dear aunt, she has often told me how they went out, her husband with his white waterproof coat over his arm, and Ronnie, her youngest brother, singing 'Bertie, why do you bound?' as he always did to tease her, because she said it got on her nerves." 

Vera knows that when the men return they will have the little brown spaniel with them, her uncle will be carrying his white waterproof coat over his arm, and her aunt's youngest brother will start singing, "Bertie, why do you bound?" When Framton sees and hears these three telltale things he will be sure the approaching men have been dead for three years and are just now returning from the bog.

Mrs. Sappleton reinforces this impression:

"Here they are at last!" she cried. "Just in time for tea, and don't they look as if they were muddy up to the eyes!"

And when Framton turns to look at Vera, 

The child was staring out through the open window with a dazed horror in her eyes. 

It is only when the three men enter the room that the reader is let in on the practical joke. Mr. Sappleton shows he is an ordinary mortal with the following dialogue:

"Here we are, my dear," said the bearer of the white mackintosh, coming in through the window, "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?"

Mrs. Sappleton hasn't a clue, but Vera thinks it wise to make up an explanation in order to forestall any inquiries Mr. or Mrs. Sappleton might make to Framton's sister, who wrote the letter of introduction, or to the vicar who must have introduced her to the Sappletons several years ago. So Vera makes up another story.

"I expect it was the spaniel," said the niece calmly; "he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave with the creatures snarling and grinning and foaming just above him. Enough to make anyone lose their nerve."

Even a girl as imaginative as Vera could not have invented such a bizarre story out of whole cloth on the spur of the moment. Her story helps to characterize her further as a bored teenage girl who is confined to this big country house all day and has nothing to do but read books. We can imagine that Mr. Sappleton, who is so fond of the outdoors and of hunting, would have a lot of books about travel and adventure in his library, and that his precocious young niece had read an anecdote about some traveler hunted by a pack of feral dogs in one of his collection of such books. Her uncle is probably not much brighter than her aunt and is therefore unlikely to remember reading about such an incident in one of his own books, if he ever did.