Notice something... a bit weird, about this ‘path to the truth’?
Shuichi points to Ouma as a suspect because of a weak point he made in the Mass Panic Debate. Afterwards, Ouma is cornered, for misleading them with a lie. But according to the way Shuichi’s logic panned out up until that point, there’s no way anyone could have murdered Angie without first entering her lab. That was the state of the situation, so it would seem that anything suspicious said by someone capable of entering, was as good as a confession.
Granted, Shuichi is not strictly speaking resolute, he’s just offering a possibility. That said, it was still his reasoning that made Ouma a suspect, and only now is he concerned about how Ouma locked the room when he left. He also does nothing to rule out Ouma leaving the room with the lock trick. There’s no way he could have been certain about that before asking him, and even afterwards, it’s only established because of how Ouma faltered in his explanation.
Basically, it was Ouma’s suspicious behaviour above all else, that made Shuichi so sure he was lying, even when that had no clear basis. He even remains a suspect, despite being called out for lying about being the culprit.
With the way Ouma reacts after being ‘caught’, the focus is almost entirely on the notion that: Ouma lied about being the killer, that he planned that lie for a reason, and that Shuichi interrupted that lie with his deductive reasoning.
But something is curious about the weak point too, because of something ingrained to Ouma- his own lockpicking. If he was accustomed to picking locks as an integral part of his group’s activities, it would be a bizarre thing indeed to outright forget that he was capable of opening the door, never mind the fact that he demonstrated it. That being: not only did he acquiesce to ‘being the culprit’, he baited Shuichi into making that suggestion from the start.
What’s more, not long after this he baits Himiko in order to shift the focus of the trial to Tenko’s murder. He uses her emotions to rouse the rest of the class, and move them to where they needed to be. It’s even spelled outright by others in the group, even acknowledged by Shuichi, that it was roundabout work.
It’s unclear as to why, but nonetheless that remains an integral part.
What does it accomplish? Well, let’s look at the end result: Ouma acquiescing the way he does, gives Shuichi more credibility, and Ouma less. With that in mind, it’s curious how he leads Shuichi with the weak point; as a detective, Shuichi’s motto is to focus on the ‘coffee-stain on someone’s back’, and a stand-out weak point in the debate was, for all intents and purposes, a ‘coffee stain’.
Given that Ouma chooses to poke at Himiko’s straggling, pent-up emotions in order to bait her... he seems to know the group and their foibles rather well, and makes a point of pressing on them. The agenda he appears to have with such actions is telling; in Himiko’s case, he dislikes the notion of her lying to herself and repressing, and in Shuichi’s case, he goes as far as painting a proverbial ‘coffee stain’ on himself in order to have Shuichi accuse him.
What it would result in, was Shuichi grasping at ways to discredit Ouma, based on his responses. Not exactly a very detective thing to do... and yet, it’s a very Danganronpa mechanic thing to do, to leap on another’s dubious words first.