WARNING: The following contains spoilers for Jujutsu Kaisen Chapter 165, "Tokyo No. 1 Colony, Part 5," by Gege Akutami, John Werry and Snir Aharon, available in English from Viz Media.
When Higuruma used his Domain Expansion to put Yuji on trial for entering a gambling parlor in Chapter 164 of Jujutsu Kaisen, Yuji thought hard about his options. He was found guilty, but to his credit he did at least think of the solution that would've gotten him an innocent verdict. His mistake in that trial was overthinking the crime and what he needed to say to be found innocent.
In Chapter 165, Yuji demands a retrial, and would've likely been found innocent after learning from his earlier mistake. However, there's no analysis at all in his second trial -- the crime he's being accused of is one he feels morally obligated to accept responsibility for.
Correctly suspecting his foe can't use his Cursed Energy, Higuruma relentlessly attacks Yuji, explaining that Judgeman's penalty of confiscation temporarily makes it impossible for targets to use their Cursed Technique. However, Yuji didn't have a Cursed Technique, which caused the effect switch to restricting his Cursed Energy instead.
So how, then, is Yuji able to stand against him without Cursed Energy? It's due to his physical prowess, which means his raw strength must be immense. Sorcerers tend to lose basic control over Cursed Energy when they're unable to use their Cursed Technique. The complete disability of Cursed Energy is even more disadvantageous. And yet, Yuji is fighting Higuruma as if they're on equal footing.
Eventually though, he begins to struggle against Higuruma's incessant attacks. Despite Yuji's ability to defend himself with superhuman strength, he's unable to make any effective offensive moves without Cursed Energy. He racks his brain to find some weakness in his opponent and figures that since his technique is based on court decisions, he should be able to get a second trial. He tells Higuruma he wants to redo the trial, and the two are immediately placed back in the Domain.
Yuji realizes that since Judgeman was the one who declared his guilt and sentenced him, he can request a retrial if he doesn't admit to a crime -- and Judgeman can't refuse. He's surprised to hear that he stands accused of committing mass murder in Shibuya -- but doesn't hesitate to say that he did it, adding that he's not lying or trying to deny it. Higuruma is shocked, while Judgeman naturally finds Yuji guilty and announces his punishment: the death penalty.
It's possible that Yuji could've used what he learned from the previous trial by denying the accusation and explaining that it wasn't actually him, which might have seen him found innocent. However, it was clear during Jujutsu Kaisen's Shibuya Incident arc and the immediate aftermath that Yuji accepts responsibility for Sukuna's massacre. He hasn't blamed Sukuna at all for the tragedy, and evidently has no interest in pleading innocence.
Interestingly, Higuruma's subtle reaction to the confession indicates he might have conflicted feelings about it. At the very least, he's confused. After all, Yuji went out of his way to lie about why he entered a gambling parlor as a minor, yet he's confessed to mass murder without even thinking about it. It wouldn't be odd if Higuruma asks for further explanation -- which just might lead to the two reaching an understanding and becoming allies.