The phrase to go off on one means to lose control of your emotions in a negative way and become excessively angry or aggressive. This is an informal phrase that is used more often in British English.

1. When I told Frank that I wouldn't lend him any money, he just went off on one and started calling me all sorts of nasty names.
2. Nobody held Abby responsible for what happened, but that still didn't stop her going off on a rant about how she always gets the blame for everything.

1. Rachel has always been a pretty laid back teacher, so I was surprised to see her go off on one about the behaviour of her students this morning.
2. The presentation started well, but then Chris went off on a tangent that led nowhere and people soon started to lose interest.