The origin of "zero tolerance" is at least in part due to the perception that when authority figures have the discretion to use common sense to decide whether an act should be punished, that discretion is often used in a discriminatory manner.
Let's say a little white girl, with no history of behaviour problems, brings a steak knife to school with her lunch from home, which includes a piece of tough meat where it can be understood as common sense that the knife was intended to cut the meat and not another student. So the teacher or principal doesn't punish the student, but merely tell her and her parents that metal knives aren't allowed, and in the future she should bring food that doesn't require one for her lunch.
Then, a few months later, a black boy known to be aggressive accidentally drops a pocket knife out of his pants at recess. There is at least circumstantial evidence that he may have been planning to use it to cut someone or at least threaten to. He gets suspended for three days. Then his mother complains, "Oh, but that little white girl who had a knife in school a few months ago didn't get suspended.... Are you treating my boy differently because he's black? Or because he's a boy?" Never mind that the behavioural and circumstantial context is different....
Zero tolerance is a "cover your ass" method to prevent accusations of discrimination. While the situation I wrote up is fictional, it's all too close to reality....