The accusation stems from the revelation of the murderer's identity, which is considered by some to be unfair and a violation of the classic detective novel rules. The reason for this accusation is that the narrator, Dr. Sheppard, is the murderer, a fact that is not revealed until the very end of the book. This twist breaks the traditional pattern of the detective figuring out the mystery, leaving the reader feeling cheated.
However, many critics argue that the novel is a masterclass in storytelling and that the twist serves to highlight the complexities of human nature and the ability of a seemingly innocuous character to commit a terrible crime.
Ultimately, whether you consider "The Murder of Roger Ackroyd" a cheat is a matter of personal opinion.