Rabu being from Trinity proves there is something fundamentally wrong with that school.
Hanako hinted about it. It's not just the constant power struggles between the the factions.

While Trinity is known as the academy for elegance and order. it can't hide that it produced quite a number of delinquents (like Kazusa) and breaks students (like Mika)

It is also deeply implied yet not confirmed that Akemi is from Trinity as well.