>Have Rin being the one to decide to throw the initial punch. Why does it matter?
It's the very first time Rin has to go against Shinji. While it may simply be an sparring session, she has to work up the will to hit the guy she is in love with, whom she respects most and that she clearly admires a little too much.
Imagine for a second how anxious Shinji would be if he had to spar with Sion herself, and you shouldn't be far from how Rin feels.
I think having her throw the first hit can play is a symbolic and essential step in the way she needs to reevaluate his skills down. For now, she imagine him as some sort of heroic man who cannot be defeated by a timid magus like her. That needs to be fixed.
Why? Because if Rin can be a source of trouble for a guy like Shinji, she can face less intimidating opponents with a more... serene heart and maybe a bit of a boost in self-esteem?
There is also the whole issue with associating initiative with punishment. That's something you see through Rin's training with Touko and the Fujou as well. Nearly every time she was seen trying to improvise, she was seen either scolded or severely punished for it.
While it was good for her to learn not get conceited, it also gave her the idea that initiatives are outside her reach. That she is not built for it. That's why she asked Shinji advice multiple times instead of thinking for herself. For her, initiative = punishment. A negative association that certainly doesn't help her growth.
Shinji must show her that no, you can show initiative and still get something positive out of it.
>Have Shinji be in the role of a military instructor. Why does it matter?
Well, first and foremost Shinji needs to rethink his way of doing things. While he managed somewhat in the past years to get by while being mostly dealing and focusing by/on himself only, he now needs to learn to think as a squad leader, and all the responsibilities that it implies.
Managing your unit's morale, overall and individually, is a prime factor in success. You want to be respected and trusted, then you need to prove that you can be there for them when it counts. Rin's barely out of the nest at this point, while she may have strong potential, her self-confidence is very low and she lacks experience.
What she needs is not another guide mind you, but someone who will push her to fly by herself. A professional on whom she can rely on to be honest and deliver a fair assessment without judging her for what she lacks. Someone who points out flaws and has her find a solution for it.
She already knows that they are much more stronger people than her. She has witnessed the harshness of that reality with Touko's puppets, with the Fujou members and knows that some anomaly like Shinji exist.
Being aggressive here, while she is most likely building anxiety at the sole idea of facing Shinji here or being trying to teach her a lesson in humility, are not ideal yet.
Aggressive and taking her out quickly will only shove in her face that she is weak / worthless. She already knows that she is lacking, no need to destroy the little ego she has left, nor put more pressure on her.
Tricking her into getting cocky is something you want to use when the opponent is getting complacent, I don't think Rin is in that state of mind right now. She doesn't need a wake up call.
On the other hand, you don't need to be nice to her nor do you need to encourage the idea that Shinji is someone invicible either.
Just do your job so she won't be weight for the team and will be able to act by herself once the situation calls for it.
Finally, Rin needs to stop looking at Shinji as her romantic interest exclusively. There's a lot for her to get accustomed to, but this is an essential point that she needs to get down. There is more to Shinji than just the boy who went to the restaurant with her or bought a house for her. He is not nice all the time, nor has he all the time in the world for her.
If he gives her a personal run down on her shortcomings, it should be something that matters, and thus she should be expected to take the lesson seriously by finding ways to circumvent her weaknesses / fix them - especially on the long term.
>Leave Rin with something solid to work with after the lesson. What does that matter?
Well, the important part is that Shinji is not simply listings a number of faulty traits that she needs fixing. He is physically go through the extra step to "mark" the moment, in order to discuss after the lesson why that was not ideal. It gives accurate image of important steps.
That's something important for someone like Rin, since magi tends to work better when mental imagery is involved.