Why I Ship SatoRyou
Ryouko
Momoi
Satoshi Miwa
OK they are dorks! They are the most pathetic, mean-spirited people in the show! They have selfish intentions in love when their objects of interest never showed anything for them! But they learn and move on. Amusingly, at the same time.
The obvious reason is that Namura's feelings for Ryouko were much like Meiko's for Satoshi. He almost could love her, but it wasn't quite right. Meiko and Namura both insisted on being given more time to make up their minds, being apologetic, when in reality they were in love with each other. In turn it would make sense that Satoshi and Ryouko would be attracted to each other.
This makes them a lot like other "Pair the Spares" in Marmalade boy, such as Arimi and Ginta, Suzu and Kei, and Tsutomo and Yayoi. Maybe they didn't pair up in the actual show, and instead did something less invasive to the main characters, probably because Miss Ryouko is an anime-only addition, but that doesn't mean they didn't have insane chemistry.
I can tell the director shipped them, even if they didn't dare let another teacher-student relationship come to pass.
Ryouko likes Satoshi, a little bit
Telling Meiko's worried maid that she'd "ask her students", Momoi-sensei immediately called Miwa-kun on the phone even when she already knew Meiko would be heading to Hiroshima. Because of this, Satoshi was able to follow her on the train. In an effort to stop her from interfering with Meiko's meeting with her older ex-boyfriend, that is.
She was disappointed when Satoshi suggestively said, "I only came so I could keep an eye on you", followed by "To make sure you don't hurt Meiko in any way". Which is to say, a small part of her wishes Satoshi watched out for her and not Meiko.
She is exactly his type!
Besides having Meiko's soft-spoken, intelligent nature, (and having a design likely based off of hers) Satoshi did ask Miki to dance with him after his rejection since she was the type not to cause trouble. Ryoko is the opposite of troublesome.
In English dub, Namura and Satoshi have the same voice actor
Meaning she's literally already in love with his voice, but on the wrong guy.
Couple of assholes
Ryouko stands idly by while Satoshi punches the life out of Namura. She yelled at him to begin with, but made no further efforts. My interpretation is that, she enjoyed seeing Namura get his due, even if he never hurt anyone directly. She probably hated Namura for never noticing her feelings for him. Wow. Then Satoshi is a psychopath for relentlessly attacking a pacific man.
Never mind that endlessly pursuing a person who is dating someone else and visibly doesn't like you back, makes you a shitty person. Ryouko was indeed, a passive version of this.
Dynamics
Satoshi is exceptionally aggressive and Ryouko is exceptionally passive in both of their respective unrequited loves. Satoshi pushed for Meiko's love even when she wanted nothing to do with him, and Ryouko never told Namura even that she liked him despite them being close friends for about ten years. Put them together with some respectful character development, and they would be attractive to one another's courage and reservation.
Endgame
They did not end up with each other. Satoshi does not get with anyone in the anime, despite recovering from his feelings for Meiko and going out with college-aged women after he graduates. He and Miki went to the dance together, since he wasn't interested in any of the students that weren't Meiko. Ryouko eventually went out with Akira, the little brother of Rei. It is implied she is recovering from her feelings from Namura. However, Akira had done the advancements on his own and when she went on a trip to Europe alone, she had sent a postcard to Miki not Akira. They were going out, but not dating. During Meiko and Naa-chan's wedding, Miki hopes that things work out between Ryouko and Akira.
Does she really like him though? With that diffident look?