I'll chime in to post a rough timeline of the events regarding Sensei before the start of the game (mind, not everything's verified) only because bob is very insisting on the 'canon' even thoug we aren't even sure of the exact canon
- Sensei grows up in the old district an befriends her neighbour Niki, we don't know everything about his family only that he has an older brother
- Sensei is molested/groomed during middle school by a teacher named Sekai who's also in a relationship with sensei's older brother (it has not been verified that the events with sekai happened during middle school but given the way she talks to sensei during good boy I think is fair to assumed that sensei must have been around 12 or younger when it happened)
- Assuming the main girl are all ~15 yo, Ami and the rest of the girls are born when Sensei was 16 yo and in highschool, by this point you could asume that sensei is still being groomed / has an affair with Sekai (some people also theorized that Sensei is Ami's father)
- Sensei and Niki begin a relationship when Sensei was on his last year of highschool / first year of college (this is mentioned by Niki herself citing the age difference, and during that flashback in 'Spotless Mind' Noriko is still a toddler, probably 4 yo at most)
- Sensei and Niki's relationship lasts 5 year until the accident (sidenote, this accident seems to have involved Kaori). Sensei was either present or arrived shortly after it happened. This left him severly traumatized and decided to leave Niki by his own volition, they were never engaged by the way
- Sensei and Ami started living together, here Ami mentions that sensei was in an incredible bad state and that she nursed him back to normal.
- Sensei eventually decides to move on and starts tutoring. Noriko's parente caught wind of it and sing her up for tutoring (this is mentioned by Noriko herself) interstingly Noriko mentions that Sensei did not wanted to meet Niki, but had no problem with her (mentioned in event 'Loxosceles reclusa')
- Maya, at a later date, also signs up for tutoring and quickly becomes close with Sensei and starts a 'fucked up relationship' (as stated by noriko) with him. So far this is the first mention of Maya, we still dont know anything regarding Maya before this, nothing about his family or her upbringing, maybe she and sensei met before hand, maybe not.
- Sensei 'chooses' Maya (whatever that means) and stops private tutoring students and disappears again. Noriko mentions that the last time she saw Sensei was 3 years before the current timeline, and he was apparently with Maya. This is also the time when Maya and Ayane became friends with Ami as she metions meeting them during middle school.
- Sensei starts teaching in his current role, and is in charge of Ami's class, something here happened that set the world to its current state but we still don't know what was (many theories, Senseis comitted suicide, Maya became pregnant, maybe another accident happened). Many loop and resets later we are at the begining of the game
So Sensei was never Niki fiance (only thing that is mentioned is that noriko a her parents believed that they'll eventually marry) Maya appears way late into the timeline and she wasn't the reason sensei left Niki, she also didn't keep her away from her that was all on sensei. She did keep him away, or at least persuaded him to stay away, from Noriko. However this is she say, the other person says scenario, Mayas says sensei choose her, Noriko say Maya kept him away.
So far we only know that Maya has been lying to Ami, as she doesn't know the previous history between sensei and Maya. So this theory of Maya is secretely manipulating everything doesn't really holds up so far.