@ wiser3754 : well Mari seems to like to push them toward one each other that's for sure!
Now, as many things that can be interpreted in different ways :
- Mari seems to absolutely love trolling Asuka(when she waited before supporting her during operation US, by calling her "Princess"...), so since Asuka used her time-off to go visit Shinji, Mari used that to troll her further, besides Asua as always been very easy to tick off, even more after the time skip!
- or maybe Mari as a plan to bring them closer : Mari could have learned more about Asuka and hos she see and feels toward Shinji from the past 14 years together(even if Asuka probably never talking frankly about it, she could have let slipped some tidbits here and there, and with time Mari got the whole picture), and from her last encounter with Shinji himself 14 years ago, she knows that even though he tends to run away from his problems, once he's in the right mindset the boy fight like a beast with a lot of courage(and it indeed take a lot of courage to fight Zeruel on close quarter!).
You can put you ship-goggle and think that she's trying to play matchmakers because she have the hunch that they are made for one each other(and if Shinji is cursed too, that makes him the only boy Asuka could date!), or even without ship-goggles, maybe Mari think that both would benefit from the other experience : Asuka would shake Shinji out of his immature and selfish bubble and make him get a hold of himself, and Shinji could help Asuka feel less alone in the world, if the theory that she's ostracized from the rest of mankind and got similar experiences of being feared and treated as a dangerous test subject are true.
From the Tsurumaki Interview in the 2.0 CRC, Mari is described as someone at the same time "wise" and "a little crazy", and her behavior certainly support this : she's very detached, take everything as a game, but can become completely serious and focused once the situation get really serious.
As for why she asked Shinji to help Asuka, Mari knows that Shinji isn't an enemy and wants to help : remember that in Lilith's chamber when Shinji talked to Asuka and said that he wanted to retrieve the spears to save the world and not finish 3I job, he was using his EVA's loud-speakers(same for Asuka, they logically don't have each other's frequency to communicate via the intercom) so Mari too heard that Shinji had good intentions and is "just" being manipulated in finishing 3I.
Besides Shinji's behavior wasn't aggressive at all : his "offensive use" of the RS Hoppers consisted to push back Asuka with their ATF, and the most violent thing he did was a slap to get her out of atop him, that's really tame compared to Asuka's berserked frenzy!
And for the "14 years" of age gap between them, if Mari's objective is just to have them mend their friendship and benefit from their respective experiences, then the gap isn't important. And even if she want to play matchmaker, we don't know how much Asuka matured with 14 years trapped in an early teenager body with her personal experiences reduces to "fight and survive", and if Shinji has the curse of Eva too, then it would be even more easy : in a little more than five years he will be an adult, and then even if he's twenty and she's in her early thirties, they both have a 14 years old body, so who cares!
But something that would be interesting to see is if Asuka really considers herself an adult : sure she calls Shinji a "brat" but she never take a point on saying that she's an adult. But if she did, that would be a very interesting inversion of her character in NGE : in NGE she was a kid(13 years old at the beginning, 14 near the end) that wanted to be treated as an adult, which only served to support the fact she's still a child, and now in 3.0 she's technically an adult(of the same age than Misato before even!), but trapped in a child body. Or better yet : maybe she don't want
to be considered an adult, maybe she wants to continue with her childhood to experiment all these new things that Misato talked about during their telephonic conversation in 2.0, but the post-N3I, her true age and probably the rest of WILLE's personnel forces her to act like an adult, which effectively robbed her of any chance of a childhood... while not letting her enjoy adulthood either since she's trapped in a child's body!
But anyway, I'm sure that Asuka's and Shinji's interactions and relationship will be pivotal in Final, every other film focused in Shinji's interaction with another character : Misato in 1.0, Rei in 2.0 and Kaworu in 3.0, now it's time to explore Shinji's relationship with the last of NGE's characters that marked him the most : Asuka.
On a side note, I would like to speculate about Rei Q in Final : in the same Tsurumaki Interview in the 2.0 CRC, he said that one of the early plans for Rei in 2.0 was to really die and be brought back in 3.0 as Rei III and seize the opportunity to really explore the theme of one's own identity when you're a clone. But finally it didn't happened like that, and I think that's because even then people would suspect that this is still "our" Rei : the series, EoE and later the CI outright confirmed that Rei I, II and III souls are the same(Lilith's) and that her memories are uploaded, so the differences in every character come from her state of mind(a childish for Rei I, since she was a child, "normal" for Rei II and nihilistic and pissed off for Rei III because she's sick of being resurrected)
And that's why adding Rei Q was a genius idea from Anno : as it has been repeated time and time again in 3.0 : this Rei is not
Rei II, nor Rei III, the later soul is inside EVA-01, so Rei Q is truly another entity only having the same kind of body than the previous Reis, and with it Anno can really explore the theme of what make someone's identity, they even got as far as make her official name "Tentative name : Rei Ayanami"! That means a lot no?
And Rei Q already started with her questioning about the fact that there was an "original" her, that she's "not Ayanami", when she saw the 12th Angel morph into a giant head with her face(complete with the killer question : "This is me? Who I am? What I am?"), and culminating at the end of the film were she lost the control of if Mark.09 and asked "What would Rei Ayanami do?" to which Asuka respond "I don't know, what do you
want?!", and that a very important passage, because that's the first time Rei Q act from her own volition, but not as "Rei Ayanami", but as "herself
", and unlike all the past Reis who were prone to sacrifice themselves, she choose to eject : she chosen to live!
Why? Because she want answers about who she is, and she must live to reach these answers, that's also why she tag along Shinji and Asuka, because they are the one who make her questioning herself.
So something I could see in Final is Rei Q asserting her individuality by changing her name and her appearance : maybe she will let her hair grow, or cut her shorter(something similar happened in ANIMA), or dye them of another color... maybe she will keep the "Ayanami" surname as an acceptance that she have ties to Yui and the Ayanami series, but will still assert that she's not "Rei" Ayanami, but Yuna/Reiko/Alice Ayanami!
Besides, that would be the opportunity to sell more figurines at her effigy!