DEsquitarse is more or less like tit-for-fat in english. Eventually it can also mean an act in which you release yourself from any feeling by doing something to someone. Gonna give u some examples for you to understand better: Clara: he tenido un día muy complicado, te molesta si me desquito contigo? José: bueno cuéntame So, she had a hard day so the only thing she wants now is to get some relief, quiere desquitarse, though desquitarse might imply that she is going to talk through about why the day she had was hard, it can also implies that she needs to punch sth or some1. Desquitarse implies to look for some relief by doing something which can be just a talk, or damaging someone, physically, or emotionally. And going back to your text, you can use to empty oneself as a synonym. Me odias y tenías que vaciarte, desquitarte, desahogarte, quitarte esto del medio,etc.

"Desquitarse: obtener una compensación por una pérdida, en especial realizando lo mismo que la provocó." (thefreedictionary) En este contexto creo que significa vengarse obteniendo algún tipo de compensación por ello.

Gracias Camilo.

Para tu información: desquitarse reintegrar, indemnizar, compensar resarcirse, vengarse, desagraviarse 'desquitarse' aparece también en las siguientes entradas: resarcir - resarcirse - vengar