You could say it's ironic because most people would presume that an unmarried man would not have a clue about children and how to entertain them. This is exactly what the aunt presumes. She even presumes that the man is frowning because of the children's behavior, labeling him as “unsympathetic” when he is most likely frowning at her and her own reaction to the youngster's question about sheep.
However, it isn't that unusual that someone like him, an outsider in terms of the world of the family, would understand the children better. How many people, for example, can remember an unmarried aunt and uncle entertaining them silly? Like the man in the story, they always seemed to have a better understanding and more unique take on the modern world.
In addition, there is no consequence to their actions. The man can tell a story about a wolf eating a girl...
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because she is just too good and then walk off the train, knowing he won't have to deal with the children later. The aunt, on the other hand, like so many parents, probably knows the consequences her words and actions can have. She may seem unimaginative in the context of the story, but she could just as easily be trying to do her best by the children.
In that context, the irony comes from the fact that the children are taken in by someone aiming to do them more harm than good.
At the end of the story the man states:
"Unhappy woman!" he observed to himself as he walked down the platform of Templecombe station; "for the next six months or so those children will assail her in public with demands for an improper story!"
References
It is ironic precisely because of the fact that a bachelor, because of his status as an unmarried man without children, should not know how to tell a story that could appeal to the imagination of children, especially when compared with the aunt, who, because of her status as being an aunt and the time spent with her charges, should, in theory at least, know how to tell a story that the children would like.
Of course, the irony lies in the way that the bachelor tells a very nontraditional children's tale, which, in the words of the aunt, "undermined the effect of years of careful teaching." The way in which the bachelor's tale and the kind of values that it presents managed to capture the attention of the children, in spite of the bigger moral "tragedy" as the aunt saw it, is another reason for the massive irony of this excellent short story. What is moral and improving is not always what is interesting.