Boy, I don't have an answer for that except to say that obviously it got infected by Acetobacter. How that happened is a mystery- could a fruit fly have gotten in there? Was there contamination on the yeast packet? Did your airlock/stopper not get sanitized properly? Did the stopper ride up at some point and allow the infection?
I'm a winemaker, so I do use Campden tablets in everything I don't boil, and I've never had an infection. But there are people who don't use them, and don't get infections, too! I'm sure that it was sanitation- but how/when will always be a mystery, at least to me.
I say try it again- use Campden tablets if you want to be sure to kill the wild things. It might not be necessary, but it might help.