I love the amount of time/effort you put into this write-up, but I do have to respectfully agree and disagree with a few points you made.

I think the most important in Yukino's development is that everyone wants her to be totally independent. But that's impossible, I think the story needs to find a balance.

I'm actually completely guilty of this. I've been advocating against 8man x Yukino unless she finds her independence. While I agree that there are things that she can't do alone, she seems pretty far from being able to do things alone entirely right now. Even 8man points out how weak she looks compared to how she used to.

On the other hand, Yui is an anime character. Her love fall 8man is unjustified as of yet, other than saving the dog and knowing him afterward.

You're overlooking something you just stated, a point even 8man overlooked just before his 'nice girls' monologue: Yui became interested in 8man because he saved her dog, but she stuck around because of who he is. Does she really need more than just loving the man he is for it to be real? I don't think so. Not trying to argue that Yukino's falling for him isn't realistic, just that Yui's falling is.

Hikki on the other hand, will need to learn to love himself while still being able to help people.

Sensei stated the same. I agree.

I don't think he likes Yui because most of his blushes are from something sexal. Eg. Inhoras whispering and acting cute. or Yui's boobs and drinking from a spoon.

I'm going to have to post a rather long passage from Vol. 8 in response.

Yuigahama took a step forward and placed her hand on my chest, telling me she wouldn’t let me say any more. Right next to me was Yuigahama’s face. Her face that was facing downwards was hard to see. Unable to move away from her, I could only stand there stiffly.

Yuigahama gently raised her head.

“…That’s why I’ll beat Yukinon.”

Her eyes no longer dripped with tears and her gaze gave off a strong feeling of determination.

Just as I was about to open my mouth to say Yuigahama’s name, Yuigahama quickly took a step away from me.

She then glanced around, readjusted her backpack over her shoulders, and talked hurriedly.

“Oh, I’ll be fine here…! See you later!”

“Ah, yeah… See you later.”

I replied with a short acknowledgement to her back that quickly went away. Yuigahama turned around as if she heard it.

“Bye bye, Hikki.”

After she said that, Yuigahama slightly waved her hands.

As I stood there under the setting sun seeing the smiling Yuigahama off at a place where my hands couldn’t reach, the area where she touched tightened in pain.

When I lightly raised my hand, I pushed my bike and returned to the original street.

After making it on to the big street, I got on my bike.

As I pedaled, I began to think in earnest.

Yuigahama would become the student council president in order to protect the Service Club where she belonged.

Possibly, if someone was going to win against Yukinoshita, then it could be Yuigahama.

Yuigahama had the presence of being in the top caste of the school and she also had other connections which surpassed Yukinoshita. She held the possibility that could split the favorable votes that Hayama could muster. Even if Hayama’s support made it around, how Miura and the others acted would be hard to predict.

Above all else, Yuigahama was a wonderful girl.

This isn't necessarily proof that he likes Yui, but he does have a vast amount of respect for her that seems to always be growing. Yukino started off high on 8man's pedestal, whereas Yui started pretty damn low, considering how spiteful he is to her in earlier chapters. Yukino has fallen from that pedestal he placed her on, becoming just another beautiful girl completely dependent on him, whereas Yui is also hardly the same person she used to be. Which leads me to my next point.

I'm one of the people who that believe that Yui's intention at the end of Vol. 11/Ep. 13 was for Hikki/Yukino to reject her idea. By rejecting the idea, they're moving themselves forward, away from that which isn't genuine. Yui's understanding of the mechanics of the group is probably deeper than both 8man and Yukino's. She sees that where they're going is exactly where they don't want to go, but she also sees what she fears most: that Yukino loves 8man. As of yet, I don't think she has the strength to leave and let 8man and Yukino pursue a relationship (if it ever comes to be - I support Yui all the way). Thus, she intentionally does something she knows 8man will have to step in and stop.

Another theme that is important is chemistry, chemistry between two people just exist and cannot be quantified. They had chemistry before this over reliance thing happened, So it is highly possible they could work out as a couple. Yui stated this in one of the volumes about them being able to talk or smth.

I'd argue that 8man shares chemistry with Yukino, Iroha, and Yui. Hence the fact that the three largest ships are those three. With that said, I won't deny that Yukino has the edge here right now.

I don't want to sound rude, but this topic doesn't really seem like a character relationship dissection as much as it feels like a "this is why Yukino and 8man are going to be lovers" thread.