Analysis – Shuichi's Perjury
Context
During the 4th trial Kokichi is trying to "prove" he didn't go to the rooftop (he's doing the opposite actually, but I've already done that analysis) and eventually Shuichi comes to the decision that he needs to make Kokichi stop lying, and to do this Shuichi decides to fight fire with fire and says:
That's a big problem.
Why?
Problem 1
Shuichi's "testimony" means that:
He didn't have an alibi for the time he spent in the salon, the same timeframe he implies that Kokichi used to murder Miu. Tsumugi -his only alibi during this trial- even says that she hadn't known he had gone somewhere else.
His alibi implies that the rooftop door was unlocked. He was trying to prove Kokichi had gone to the rooftop, afterall.
The stairs to the rooftop were right next to the salon.
By Shuichi's own "testimony", he was in the correct timeframe to be the one who murdered Miu and he could have been in the correct location as well, and absolutely no one would've been able to say he didn't because Kokichi "wasn't there" to see him and Tsumugi admits that she didn't see him just moments prior meaning that, for all anyone knew, Shuichi could have lied about where he went and killed Miu on the roof.
The problem is that no one noticed or even pointed this out even though they all said that they believed Shuichi's statement over Kokichi's, despite the fact that it was proven that Kokichi couldn't have killed Miu. They were all too busy trying to pin Kokichi as the culprit to even consider that it could be anyone but him, and since when has anyone ever thought of Shuichi as a prime suspect since Chapter 1? They haven't.
If Shuichi's "testimony" wasn't a lie he could have murdered Miu and no one would have suspected a thing because they blindly believed in Shuichi and hated Kokichi.
Problem 2
My other (slightly less important) problem is that Shuichi had gotten so caught up in trying to find the truth, that he forgot to look for the actual culprit.
Kokichi's avatar settings were already brought up and discussed before Shuichi lied, but Shuichi is still suspecting Kokichi of being the murderer despite knowing he couldn't have done it. He even lied to try and make him "confess" to what he did, even though Kokichi couldn't do anything.
Even if it was only for a moment, Shuichi still tried to fit the suspect to the crime instead of letting the evidence lead him to the culprit, and that's incredibly stupid and dangerous when everyone's lives are on the line. Not that anyone -including Shuichi himself- noticed what Shuichi was doing, because they were all doing the same thing.
Bias Rant
Chapter 4 revealed everyone's harmful biases, including Shuichi's, but they were never really discussed or mentioned again despite the glaring danger.
Kaito was the most obvious and harmful example of this. He fought facts and logic with pure hatred towards Kokichi but the cast didn't even fault him for it, Maki (and Shuichi) even blamed Shuichi for Kaito's attitude towards Shuichi after the trial instead of blaming Kaito for being stubborn, bullheaded, and unwilling to admit to or apologize for his faults after that trial.
However, while Kaito might have been the biggest example, the others aren't off the hook either. They also didn't find fault within themselves despite trying to suspect someone who was innocent just because they didn't like him, even though they all could have literally died for not realizing their bias.
Chapter 4 should have been the best moment for them to realize "hey, I almost died today because I didn't try and find the truth and instead tried to make the truth fit what I wanted it to" and learned better than to do that and grow past their flawed thinking in order to survive, but no, they didn't even think about it.
I'm so frustrated.
I really wish the narrative would talk more about how the cast alienated Kokichi (sometimes understandably, sometimes taking it way too far) and how even Shuichi has been shown time and time again to be biased during trials while everyone else puts their faith in him and their lives in his hands. It would be an interesting plot point to have everyone go from blindly following his deductions to doubting and suspecting him after realizing he's also flawed in the same way they are.
It would also mean that Shuichi would have to develop past his biases and become a better detective to earn everyone's trust back, if he even could earn it back after being so unknowingly flippant with their lives. I think it would have been more relevant and true to the theme of the game than what his character arc actually was. Maybe they wouldn't have dragged their heels with it either–