After the initial fight and the initially training, Shinji and Asuka are having problems with their dance/synchronisation routine.
After a complaint (from Asuka) Misato, asks to Asuka "Then you are giving up?" with Asuka responding "It's not like you have anyone else"

Then we see Rei having a go with Shinji and she is pretty flawless on her first attempt. The thing is, Misato already had a smirk on her face when she asked Rei. Suggesting she probably knew Rei could dance.
Then Misato says: "Should I alter the operation to pair Shinji and Rei".

This to me made little, because only Asuka can pilot unit 02, but both Rei and Shinji can pilot unit 01 (In the Anime Rei says so in episode 6) (unit 00 is being upgraded).
This made me wonder why the pairing of Rei and Asuka was never considered?

folllow up question:
Was letting in Toji, Kensuke and Hikari in the apartment a d*** move? The pilots are under enough stress or would you say that especially Asuka thrives under such conditions?

My first thought was that Misato knew that Asuka and Rei don't get along that well. But Episode 9 was too early to know how their relation was (in fact that scene was one of the first ones to make Asuka hate Rei).

The second logical answer is that Rei can pilot Unit 01 but Shinji synchronizes better with it.

In any case, is an interesting question and could be a funnier timeline (and more Yuri).

They probably considered putting Rei in EVA 02 - the possibility is explicitly brought up in ep 10, too.

The reason Rei wasn't considered in the first place is that EVA 00 was under repairs at the time, and obvsly her synch rate with either of the other EVAs would not be as high as that of their designated pilots.

The advantage of using Asuka & Shinji is that both of them have high synch ratios. After all, the plan requires acrobatic jumps & complex movements.

Shinji & Rei had proven that they could pull of successful cooperation against the laser angel.

If you made Rei & Asuka do it you wouldn't have either advantage, no cooperation & no using the two best pilots.
If you're going to have to force Asuka to work with someone, it might as well be the guy with the higher synch rate who previously worked with her against Gaghiel.

As for letting in the classmates, generally having your friends visit tends to reduce stress and I don*t think Misato let them in for any other reason that that (in fact Hikari inadvertedly saved the day by telling Shinji to go after her leading to that little bonding moment)

I do think that Misato meant to bring Rei mostly as a way to motivate the other two (you might notice that she's got a clipboard & that she was watching the routine earlier ) and that this was probably a mistake. She knew that Asuka is competitive, but I don't think Misato grasped at this point that she got this huge existential anxiety over her position as a pilot.
Though I'm not sure that Misato could've known this at this point nor could she afford not to have a backup plan he the fate of humanity is on the line
Having someone else offer to do it worked well on Shinji cause it took off the pressure & gave him a chance to consider what he himself wants & not just what others want of him, but for Asuka this probably felt like a serious threat to her very identity like everything she worked for was going to be taken away & this probably contributed to her hostile competitive attitude towards her fellow pilots & how her relationship with Misato didn't progress past a superficial level.

I think you misinterpret Misato sentence, she said if it was possible they would have choosen Shinji and Rei, but I'm sure Misato knew it was useless to even try. Aftherall they didn't even make an attempt in episode 14 to put Rei in Unit 02.

Rei having a lower sync rate then Shinji at this time is also uncertain. In episode 14 when Rei activates unit 01, they say her sync rate is nearly the same between unit 00 and unit 01. https://wiki.evageeks.org/Synchronization
and Shinji only surpasses Asuka in episode 16 assuming Shinji would have surpassed Rei sooner but not necesairly before the events of episode 9. That said during the battle of ramiel did Shinji take the shot because he had a higher synch ratio with unit 01 or because unit 00 was still buggy and they wanted a tested pilot I've forgotten.

I sortof agree with all the rest

Shinji surpassed Rei in episode 6 - it's mentioned as the reason why he gets to shoot & she gets the shield, in that scene where everyone's silhouetted in those flood lights before they go change into their plugsuits

Pshinji wrote:My first thought was that Misato knew that Asuka and Rei don't get along that well. But Episode 9 was too early to know how their relation was (in fact that scene was one of the first ones to make Asuka hate Rei).

Does Asuka really hate Rei? She is annoyed by her and at a certain point she hates everyone, including herself but this is more of a mental breakdown I think than any specific hate for Rei.

Shinji surpassed Rei in episode 6

Yes you are right I checked.
Shinji was also pretty mellow about fighting the angel(s). So I can see why they did not suggest putting Rei in unit 01. I'm going to guess further that Rei was present during the exercices as an emergency replacement for Shinji (if they failed to cooperate), but they did not want to tell Shinji because of fears he would fail deliberatly.
So Rei is less perfect then she appears to be. Whilst it was the first time she was present in the room she had been training just as long as Shinji and Asuka probably using camera footage.
And, Misato's nonsensical lie, was to prevent Shinji from knowing the truth and it came out wrong at Asuka's expensence and she was to hurt to see the truth.

This option makes the most sence to me. It explains why Rei is such a good dancer; why she isn't doing anything more constructive; why she doesn't suggest pilotting the eva; Misato knowing Rei is a good dancer and Misato's weird wrong statement.