TL;DR @n meowzers: She was born with the ability, and she had some weird fascination (described as an 'admiration') with blood (possibly an indication that quirks change a character's propensity to respond in a certain way? Toga's backstory seems to prove as much). Society at that point (~15-16 years before the beginning of the series) thought of blood-based quirks as reprehensible (idk if the society at the current point in the story still thinks that). As expected, she was ostracized, leading to the creation of some sort of emotional mask (Sociopathic in nature, perhaps). She then ended up sucking a male student that in her school (not in a sexual way, but her face appears like it was), and ended up fleeing to the streets.
