What is the irony in "The Summer of the Beautiful White Horse"?

The irony in the story has to do with the idea of honesty and what it means to be "honest." Even though the Garoghlanian family is "renowned" for its honesty, Mourad steals a horse for the thrill of riding it. Aram finds it hard to believe that this could be the case—how could a member of his family steal?—but in fact there is a certain disconnect between how the tribe self-identifies (they were "proud first, honest next, and after that we believed in right and wrong") and their actions. Mourad is one of the "crazy" members of the family: "every family has a crazy streak in it somewhere, and my cousin Mourad was considered the natural descendant of the crazy streak in our tribe." The theft of the horse can be explained as Mourad's craziness coming out or as a way for him to discover his "way with horses." Either way, the brothers' secret is made possible, in a way, by their reputation for honesty. When the horse's owner catches the boys with the horse, he says that even though their horse is the "twin" of the stolen horse, their family's reputation for honesty will keep him from suspecting them of theft. And Mourad's training of the horse does benefit the owner; when the horse is returned, he notices how much better behaved it is. So even though Mourad did steal the horse, the outcome of this theft was beneficial for everyone concerned. As Mourad's "crazy" uncle Khosrove would say, "It is no harm; pay no attention to it."

In "The Summer of the Beautiful White Horse," the irony lies in the fact that Mourad, a member of the Garoghlanian family, steals a white horse. This is ironic because the family is locally renowned for its honesty. In fact, as Aram tells the reader, honesty is their second best-known family trait and it has been around for centuries, long before the family ever became poor:

"We had been famous for our honesty for something like eleven centuries, even when we had been the wealthiest family."

For Aram, it is unbelievable, then, that a member of his family would demonstrate such outright dishonesty by stealing a horse. But knowing the poverty of his cousin, there can be no other explanation.
Moreover, that Mourad describes his understanding of the horse as "honest" is also ironic because his relationship with the horse is based on theft, which is an act of gross dishonesty.