I'll elaborate further later, but briefly, for me, Yuu's only real flaws (and again, he is the only one real victim here) have been:
1) His jealously guarding the fact that he failed the exam from Hikari. In my opinion, this is far worse and shows much more of the open distrust he feels for a girl he still loves, even though he knows he should have gotten over her, than hiding the entire traumatic relationship he had with Yami. Especially since it had to be revealed by a random dude that Yuu and Hikari hadn't seen in years; at least with Yami, it was Yami herself who revealed it to Hikari. And if we're talking about "failure", the relationship with Yami was also a failure, which Haru herself mocks for how brief that romance was (six months). It's not a memory that makes sense for Yuu to be proud of at all.
1.1) A reminder that throughout the entire WN, Yuu never denies having had a girlfriend. Hikari never asks him if he's ever had a girlfriend; he only says he's never received a girl's confession in chapter 1 (which was true until Hikari saw Seki confess to Yuu in chapter 12). He doesn't say it even in his confession in chapter 38. However, his "I've loved you for a long time, Hikari" could certainly have been interpreted that way, and this is what Hikari believes is a lie from Yuu. (And to be fair, is very ridicuoulus and a "I have to see it to believe it" thing, all that of Yami accepting being Yuu´s girlfriend after learn he feels attracted from both her and other girl).
2) Yuu messed up in chapters 36-38. He admits it himself in chapter 38 after Hikari pushes him. "I was definitely the worst today, wasn't I?" (a very typical line from Haruki Kitahara and Yuu Izumi. Taa-kun is an Expy from both of them). It's clear his "dead telephone" little lie was to convince Hikari to go home (to cry more because Ayami had finally dumped him) and that he hadn't expected Hikari to drag him to the dance at the gym. At this point, his plan was NOT to confess; he was too depressed and just wanted to go home. Even so, even after the dance and Hikari carrying him to the gym, he chose a bad moment to confess, and he probably knew it, so he acted in "now or never" mode.
2.1) Even worse, although it makes sense that he believed Hikari didn't see the kiss and didn't say anything about it, he now knows that Yami and Hikari are friends. Therefore, now and only now is it a matter —from his perspective— who concerns Hikari. Before this point, he had all the right to doesn´t say nothing to Hikari while she wouldn´t ask directly about it -so, he didn´t lie, he only was ambiguous with a girl who was just his friend and no more-. Thus, he should have said, "I dated a girl from your school, named Ayami Matsushita/Sudo, in first year. She is the ex-girlfriend you questioned me about when I said you about Seki (this happened in chapter 18). Anyway, she dumped me after a few months and broke my heart" as part of "the efforts I made to get over you, Hikari", and hoped that Hikari would recognize the name.
Anyway, it's amusing to see Hikari being haunted now by the same ghost that once haunted Yami, what Seki called "accidental two-timing" (polygamy), and it's probably the real source of Hikari's anger —knowing that "Taa-kun" now loves two girls at the same time: "Aya-chan" and her. She has legitimate doubts about whether Yuu chose her over Ayami, or Yuu just confessed to her as a backup plan after Yami dumped him. All of which still doesn't excuse her selfish, immature, and spoiled behavior. Hikari is obviously playing hard to get. Hikari's forgiving and understanding side only kicks in when she's begged for it, something Yami picked up on very quickly (chapter 34), and the reason why Hikari acted so selflessly, protecting the more whiny Yuu when he was a child. That's why she ran out of the gym; she couldn't endure the look of obvious pain on Yuu's face at that moment.
That's the only real reason why Hikari is compatible with Yuu and Yami, at least as a friend. They're both such crybabies. And remember: still right now Hikari is still caring for Yami and still wants she return to classes and probably she will see with good eyes Yuu is trying to make Haru and Yuki to convince "Aya-chan" to return to school. Of course, I hope both Yuu and Haru never say to her about the infamous "Yami-senpai did nothing wrong" phrase -and yes, IMO Yuu got the typo after Haru lecturing him-.
And yes, at the very least, she shouldn't have pushed Yuu or helped him up from the floor —assuming the violent push was unintentional— if she really wanted him to chase her down and come to her house to "explain everything." People here, in order to avoid admitting that Hikari messed up by PHYSICALLY ASSAULTING YUU, made up a story that she supposedly had a grand plan and was going to go back for Yuu as soon as she found Yami and "Aya-chan" told her everything... which obviously didn't happen. This proves that Hikari wasn't planning on seeing Yami in chapter 41, nor did she expect to find her still at the scene of the crime —her classroom— after all that time.