What exactly was Yui trying to do at the end of OreGairu season 2?
I interpreted it in three ways:
Which one is right?
My own interpretation is actually different from any of the ones you've listed.
We discover over the last few episodes of Season 2 that Yukinoshita has a lot of trouble even identifying what it is that she personally wants. Where Hikigaya has to have an external reason to help people but is otherwise incredibly self-sufficient, Yukinoshita needs an external reason to do practically anything at all (mainly via her mother and sister), and once she has an external reason she forces herself to conform to it. Yuigahama may not be intellectually bright, but she's incredibly perceptive when it comes to people's emotions and social cues, and she has picked up on this fact. She is also perfectly aware that Yukinoshita is starting to feel romantically inclined to Hikigaya, which puts Yuigahama in a very difficult place: she wants to maintain her friendship with Yukinoshita, but the entire reason she befriended her in the first place was to get close to Hikigaya in a way that won't cause her to be judged or ostracized by her social circle.
Additionally, Yuigahama is aware that Hikigaya is undergoing an emotional shift of his own and is allowing himself to become closer to both her and Yukinoshita. This is simultaneously thrilling (because it means that she has successfully gotten him to notice her, finally) and terrifying (because she recognizes that she's in a love triangle, and him choosing one of the girls is going to destroy their current social relationships no matter what).
So the question becomes: how can Yuigahama gain what she most wants (a romantic relationship with Hikigaya) without destroying their current social dynamic? Well, first off she can't come out and explicitly confess to Hikigaya. No matter how he responds to that, their social dynamic is dead (this is the same problem that came up with the Ebina/Tobe interaction earlier in the season). Additionally, she is feeling guilty about taking advantage of Yukinoshita's obvious lack of experience when it comes to dealing with romantic feelings.
The answer that she arrives at is her double date (cherishing and celebrating their current social dynamic) and the final confrontation with Yukinoshita (which may destroy their social dynamic).
The trouble is that because Yuigahama cannot explicitly say what she wants to say, we have to rely largely on subtext. As I read it, the subtext goes like this:
And at this point, Yuigahama has won the love triangle match. Until, that is, Hikigaya interjects with his insistence that Yukinoshita needs to solve her problems on her own or she will never escape the cycle she's currently stuck in.
At which point the really fascinating part of this scene occurs, which is that Yuigahama says she thought he would respond that way and immediately backs down. The implication here is that Yuigahama entered into this whole gambit believing that she would probably fail, but did it anyway because she did not think the status quo was maintainable and that forcing her friend and her crush to face the emotional currents that underly their little threesome was desirable even if it leads to her losing Hikigaya.
Both Yukinoshita and Hikigaya are very alike in a lot of ways. Needless to say, both Yukinoshita and Yuigahama have amazing quality and are wonderful friends, but the longer it takes, the more painful it could get. I can see this being a huge problem considering the situation.
I myself couldn't agree more with Hikigaya's interjection, If he didn't say something, Yukinoshita would have lost much more then just a chance with Hikigaya. At the moment, she is going through a change and needs time. It's important for both to finally come out with there feelings. But, if Yukinoshita can't get her own thoughts and feelings together, she won't be able to decide for herself. They can make it known to Hikigaya their true feelings and put the ball in his quart finally. He may be dense but I think he fully understands the situation and needs a bit of a push to come up with his own desires. In the end, even if both or one backs down, it's still up to Hikigaya to find his own path or decision.
We have to remember that Hikigaya has a history or even a little post-traumatic stress when it comes to rejection. I mean we have met two other women in his life who have rejected him. So, this could be a bit hard for him as well. Someone's bound to get hurt either way which sucks I believe.
I thought maybe Yui was proposing sharing Hikigaya, as there were hints that they had come to an understanding about him.
That part where Yui sits uncomfortably close to Yukinoshita seems to suggest a particular change in fondness. I thought this was indicating possible yuri, but she still likes Hikigaya and she also knows Yukinoshita likes him. If everybody likes everybody, why force a choice.
I think she actually thought that if anyone of both yui or yukino confessed their feelings for hikigaya then it will disturb there friendship and they won't be friends like they were then, so she meant that if she tells yukino about what to do with her problem then she will win the battle royale and yukino and hikigaya would have to do what she says which is to drop her (yukino) feelings for hikigaya as she (yui) was ready to do and remain best friends forever with hikigaya and no one would confess their feelings for hikigaya. The gist is that she wanted to maintain the status quo and not to disturb it. She felt that their friendship was important than her love and wanted to keep it. she was like the problem is having a romantic relationship with hikigaya (for both of them as if one got into a relationship the other one would feel jealous and ruin the perfect friendship they had), so why not remove the possibility of that and remain friends forever.
