Imasara desu ga, Osananajimi o Suki ni Natte Shimaimashita - Ch. 43 - The Pride of the Lecturing Girls

[peortega1]

I would point out that if he paid a bit more attention he'd notice that Hikari wasn't seeing anyone in a romantic light (based on her rejecting anyone who confessed to her at the end of middle school) and if he had a bit more emotional maturity he'd realize she's not rejecting him because he's not good enough, she's rejecting anyone because she's not at a point in her life where she's capable of feeling romantic feelings.

Ironically this securely reforced his insecurities. If other boys of the school, who he probably saw as better than he himself, failed in his proposals to Hikari, why he would have better luck?
And again, Yuu was DISPAIRED to have a girlfriend. Is very logical he looks for other girl if he notices correctly Hikari in this moment doesn´t want to be the girlfriend of anyone.

All this is to say that Yuu's default response is to almost always assume the worst.

Of course. Other reason why he is an Expy of Yuu Izumi... and other thing both Yuu shares with all the Maruto male main characters. Low self-esteem, pessimism, always first blaming to themselves instead other people... Haruki and Tomoya had all these features, and in a worse decree.
The positive side of all these features is they will make much more easier his reconciliation with Hikari.

When Yuu failed the entrance exam to Hikari's high school he immediately jumped to the conclusion that he had no chance now to win Hikari's love

He didn´t "inmediately" jump to that conclusion. You are still ignoring the distorsion deliberately introduced by Ayami. Without her, Yuu probably would have return to his house, cry a lot in his room and, passed grief phase, think in a new approach to try to close to Hikari.
Ayami is the real reason why he decided renounce to Hikari and try to start again with this girl who seemed be the careful, loving and dominant girlfriend he always wanted. And to be fair, Kamiya/Ayami really was a good girlfriend for Yuu and the breaking up was mostly by external locus reasons.
Yes, distorsion. Even after accept being the official girlfriend of Yuu, Ayami is fully aware of how she is deliberately separating Yuu from Hikari. This is the reason why Yami self-identifies herself with Utaha and she is equally decided to make his boy to forget definitely to Hikari/Eriri.

 

[peortega1]

(despite literally living next door to Hikari and having the potential to see her every day and slowly build up a romantic relationship or at least get her to see him in a different light).

He has lived next door to Hikari during already four/five years and he didn´t reach nothing. He made several tries -or at least, this is hinted in both his chapters and Hikari chapters, so at least he thinks he really tried several times- and he failed.
Again, you are basically asking for other Kazuya simping other Chizuru, rejecting better options genuinely interested romantically and sexually in him.

 

[story645]

, I am claiming he never thought that.

During the second confession chapter, he gives it as one of the reasons he never confessed:

Hikari: "You thought I wasn’t thinking about you at all, Ta-kun?"
Yuu: "I didn’t think it was nothing, but... I wasn’t sure if it was that kind of feeling."
Hikari: "Come on! Ta-kun, seriously, you have no confidence!"
Yuu: "But it’s you, Hikari! Do you really think I'm good enough for you!?"
Hikari: "I do!"
Yuu: "That’s just you being mistaken! No one knows how amazing you are better than I do!"

her immediately recognizing him trying to hide his crush behind this catching up.

Or she just recognized he was talking about a crush b/c Yuu didn't specify & it could have also been a rivalry:

"There's someone I want to catch up to. To stand next to. And they're there."

Oh, okay, this one's serious.

"A girl?"

But also both can be true - he has a crush and he feels he needs to catch up. Yuu says as much in 17:

"Look, I might not have told you everything I feel, but what I just said... every word of it was true."

I'm saying that the exam saga would've happened regardless of him idealizing Hikari or not

Maruto has Yuu talking about "catching up to Hikari" in two confession to Hikari chapters, one of which is about the exam, & one confession to Aya chapter & thinking about it in the novella chapter about the exam. That level of repetition & constancy of context strongly implies that these feelings are intermixed w/ Yuu's romantic feelings. Which strongly implies that the reason why Maruto writes Yuu deciding his "grand romantic gesture" has to be taking the exam into her school rather than any of the myriad other options available.

 

[UdenEmpati]

We definitely went through this once already - this is where I bring up him saying the same to Yami and her immediately recognizing him trying to hide his crush behind this catching up.

Is it not possible that it can be two things? Also he obviously has a crush on Hikari; that doesn't preclude that he could also think he needs to "catch up" to her.
He himself says that he's always considered her out of his league when he finally confesses to her. Maybe that's his words, not "actions" as you keep stipulating, but I fail to see how it's not the case when Yuu himself says as much.

 

[peortega1]

By the way, after several re-reads, I'm surprised no one has mentioned Haru's... chemistry with Yuu. She spends the entire episode lecturing him, asking him questions, and ordering him around like she's his mother... and he OBEYS. RESPONDS. He generally appears submissive and receptive to her... just as he did earlier with Yami.
In this single chapter, Haru showed more initiative and assertiveness than Hikari had in the entire series, flashbacks, and extra chapters. And Haru spoke more directly, clearly, and explicitly, displaying a sense of monogamical moral that clashes with Hikari's almost polyamorous spirit —she also being the one who criticized Hikari's co-dependency on Ayami.
Haru must have begun to realize what kind of buttons Aya touched on Yuu, between what he said and what she might remember from Yami's "stories" about her sex life.
I'm starting to think she's destined to be the Megumi Katou, the Shino Kiryu, the Miyako Shikimori, of this story. Yuu's true soulmate. The Third Heroine.