Okay, this page is gonna be a little bit different than my usual because I just love switching things up and not doing the same thing over and over again. So in this page I'll do a quick rundown on the events of Mitsuru's Social Link, and also how to get it started because, well. It's not the easiest to start.
To start, Mitsuru's Social Link cannot be unlocked until--at the earliest--November 21st. You must also have max knowledge and gotten first place in an exam in order to even get the first link started, so be sure to level yourself up and do lots of studying to get that knowledge maxed!! Mitsuru is available on Tuesdays, Thursdays, and Saturdays, save for story events that cause her not to be around. She is located next to the Teachers Lounge on the first floor.
I will be using the female protagonist's perspective on this, referring to her as Minako for clarity's sake. (Though the only real difference is the male option has the opportunity to date her, but that's another issue entirely that I probably won't touch on because ~opinions are bad~)
The Social Link
Mitsuru's Social Link follows her through some of her social lacking, as well as her troubles with an arranged marriage. During her social link, Minako helps her overcome some of her difficulty with proclaimed 'normal' teenage activities, such as eating ramen and other fast foods.
Eventually, you will come to understand that Mitsuru is in an arranged marriage with a man to benefit the Kirijo Company but is torn about whether to go through with it or not, because if she does! No college! Mitsuru does look at the arrangement through a different glass than most would however, and sees it as a mutual arrangement that will benefit the Kirijo Group. Despite that, however, she still struggles with it.
Slowly, Mitsuru opens up about her fears of the marriage, and also as a person. She expresses her seldom distaste for her responsibilities and wanting to run away for a bit. She just wants to be a normal teenager, but she knows she can't do that. Still, she feels comfortable complaining and griping to Minako about her worries.
Shortly after this conversation, Mitsuru's "fiancé" shows up and demands her time, asking her to break plans to Minako at the drop of a hat for him, claiming she needs to "adjust to his schedule" because he's such a busy man. He even makes a comment about he's glad Mitsuru's father is no longer alive, but that isn't the final straw for Mitsuru.
You have an option afterwards of stopping Mitsuru from going with him, and she is actually very happy that you do. However, it is when he begins to be belligerent and berate you that Mitsuru has had enough. She stands her ground and announces the engagement and the deal with the company is off.
In the final Social Link, she gives Minako the key to her motorcycle as a gift of esteemed trust. She even calls you a younger sister!