Spoilers follow for the complete case, including the culprit and the false-alibi scheme.
The Sister Troubled By Her Naughty Brother is international episode 1197 (Japanese episode 1139), an anime-original case. Satsuki Makabe kills Doba and tries to frame her younger brother, Yuto. The central trick is that Yuto tells the truth: his refusal to confirm her alibi is exactly what she wants Kogoro Mouri to misread.
The case first presents Satsuki as a woman harassed by an unpleasant brother. It then tempts Kogoro to reverse that impression and imagine a loving sister protecting him. Conan has to question that second, more sophisticated-looking explanation too.
The defamatory flyers establish the wrong relationship

Satsuki comes to the Mouri Detective Agency because someone is putting up flyers at her apartment building accusing her of an affair. Kogoro catches the young man responsible during a stakeout. He turns out to be Yuto, her own brother.
Yuto blames Satsuki for a money-making proposal that left him in debt and forced him to flee his creditors. He also resents her refusal to lend him money. Kogoro wants the matter taken to the police, but Satsuki settles it by having Yuto sign a written promise.
That incident matters beyond its unpleasant family atmosphere. Kogoro has personally seen the brother harass the sister, so he already has a persuasive explanation for any later hostility between them. The flyers appear to supply the emotional frame through which he will read the alibi dispute.
A murder makes Yuto’s denial look malicious

A few days later, Doba is found stabbed in a luxury apartment. He has made many enemies, and Satsuki is among the people with a grievance against him. An anonymous woman calls with information about a suspicious woman, drawing police attention to Satsuki. Her past also includes the loss of her fiance in a traffic accident.
Satsuki says she was with Yuto around the relevant time the previous afternoon. Yuto insists he met no one and stayed in his room all day. Even Kogoro cannot persuade him to change his account. If the earlier harassment is taken at face value, this looks like another deliberate attempt to hurt his sister.
Satsuki remembers Yuto using a toothpick when they supposedly met. Conan and Kogoro therefore check nearby restaurants, hoping to find someone who saw him. The inquiries lead nowhere, and the police cannot find witnesses who support Satsuki’s movements either.
Why Kogoro’s apparent insight is part of the trap

Satsuki keeps emphasizing how badly she and Yuto get along. Kogoro begins to suspect that the feud is being exaggerated: perhaps the siblings are actually close, Yuto committed the murder, and Satsuki invented their meeting to protect him. Conan remains uneasy with that explanation.
The revealing point is that an untrue alibi does not automatically identify the person it supposedly protects as the murderer. Satsuki is counting on Kogoro to move from her conspicuous lie to precisely that conclusion. Her performance offers him a hidden family bond to discover, while concealing the much colder reality.
The truth behind the anonymous call and the creditors

Conan gathers the people involved in a park and explains the truth through Sleeping Kogoro. Satsuki killed Doba. She also made the anonymous call that initially cast suspicion on herself, setting up the investigation she hoped would ultimately turn against Yuto.
Yuto really had stayed indoors. Satsuki had given his address to his creditors, whose arrival prevented him from leaving. His truthful denial of meeting her was therefore built into her plan, rather than an obstacle that happened to arise afterward.
Doba’s overheard remarks are presented as the immediate trigger. Her final rejection of her brother is especially bleak: she makes clear that her dislike goes back to childhood. There is no protective sisterly love waiting beneath the quarrel.
Why the ending is so bitter

The episode’s strongest reversal is not simply that the apparent victim of harassment becomes the culprit. It is that the investigator’s effort to see beneath an obvious story can itself be manipulated. Conan appears to succeed by refusing to treat a clever alternative as proven merely because it is less obvious.
The flyers, the failed restaurant inquiries and the engineered confinement all contribute to that reversal. Yuto is unpleasant in the opening dispute, but that does not make him a murderer. The distinction saves him while leaving the family relationship thoroughly broken, which gives the title its cruel aftertaste.

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