Theory: Rabu is actually from a super wealthy/powerful family

And by wealthy, I mean Nonomi levels of wealth. Given that she used to attend Trinity, it can be assumed her family is fairly well off at minimum.

As for why I feel this way, there's a number of points about her that give me this vibe. First is her apparent school being Trinity. She stated she had no choice but to go there, then dropped out because she felt it too oppressive. Why was it that she had no choice? We don't see other students complaining they were forced into their respective schools. Even ones like Abydos and SRT that are in dire straits those girls still want to stay.

Her saying she had no choice also reveals why she chose to drop out rather than transfer schools, which is an option as we've seen with students like Azusa and Pina. She could've just went to a school that fit her better, like Gehenna if she wants to be a troublemaker or Millennium because of her love of baseball.

I also point out Millennium because contrary to what the world views her as, Rabu is not stupid. The opposite, in fact, as one of her friends mentions she's really good at studying. Also in the Say-Bing event, she independently refers to the mechagator as the "Cybernetic Rapid Ordnance Carrier", like Kanna had originally planned on referring to it based on observation of its traits. Meaning she has similar levels of observational skills.

So she would actually fit in Millennium fairly well due to her inherent ability to identity their technology, yet despite that being a good school she still chose to drop out and be homeless.

So my theory is that her family is quite powerful and wanted her to be prepared for high society, so she had to go to Trinity as that best fits the concept. She is a gifted student, so she probably was trying at the start, but got burned out due to the atmosphere and pressure from family. So in an act of rebellion, she dropped out and became a thug, which also meant she got disowned and no longer has money.

Other point to note is that she hasn't been a thug for long. Since she's only 16 and we know she was in Trinity for some amount of time. Since she hasn't been a thug all her life, it does show in some aspects. Such as her weak grip strength despite probably being the second biggest baseball fan among the cast (though considering Rei being the biggest fan and sucking at it means this point isn't as strong). Also her favorite gifts are workout equipment despite not being that strong, indicating she's trying to get stronger.

Lastly is her attitude. Rabu, despite her reputation, isn't a bad person. She basically spells out who she is in Magical Girl Heavy Caliber when she says she doesn't need permission to do good. Rather at this point in her life, she doesn't feel the need to do things because someone else told her to do it.

TL;DR: I hope we get a event to confront such a past with her so we get Dress Rabu alt.