I do not support Zero Tolerance policies.
That said, there were a few understandable reasons that helped them spread that I haven't seen anyone mention. As with so many school policy changes, it's important to remember the Columbine shooting and the panicked reaction to it. Teachers used to use a lot of discretion, which in practice worked a lot like the discretion cops used with domestic abusers: just dismiss things as "boys will be boys" or "it'll toughen them up" or "all families fight." Remember these policies got really popular 20 years ago. Teachers let a lot of stuff we now consider dangerous warning signs slide because things were different when they grew up. They were failing to punish kids for bullying, and one way to stop that was to take the decision out of their hands (just to stick with the cops and domestic violence analogy, this is like laws that were passed that tried to require cops to arrest someone for violating a protective order).
No one wanted to be the school where a teacher saw a weapon, said nothing because they didn't think it was a big deal, and then later the student shot someone. And no one wanted to be the school where a kid was being bullied and then killed himself/others (the kids in Columbine weren't bullied, of course, but that narrative was firmly there), only for the teacher to just be like "I thought he needed to learn to stick up for himself." And I don't know if you've ever tried to convince people that the way things were done when they were a kid were wrong, but it's tough, hence completely non-discretionary policies. Then it snowballed as a liability shield.
(The other analogy is to Mothers Against Drunk Driving - started as a movement saying "we can't keep sweeping this problem under the rug and letting individual cops decide whether or not to take this seriously" and then blew up into effectively a neo-Prohibitionist group. It outgrew its problem (in the sense that drunk driving is taken very seriously now) but couldn't just go away because people were dedicated to it now. Road to hell, good intentions, &c. &c.)