Euripides' Medea tells of the trials and tribulations Medea faces through supporting Jason, taking care of her family, and finding solace in her revenge. One could support Medea's actions in two very distinct ways. First, Medea believes that love can make people do crazy things. Second, revenge is one of the strongest motives for action.
In regards to love, Medea commits many murders (her brother and Pelias). She finds that for her to get to and be where she needs to, she must do certain things. Once her marriage to Jason falls apart, Medea realizes that revenge proves to be a far stronger emotion than love. Medea shuns all others, even her own children, to find full revenge.
Therefore, one could argue that Medea's actions are justified by her emotions. Emotions are a very difficult thing to control at times. Love can lead people to make very controversial decisions, and revenge works in very much the same way. Regardless, one cannot control whom he or she falls in love with. That said, he or she cannot control (at times) what will be done to protect the love. When that love goes astray, the person can feel that nothing is left. When nothing is left, there is nothing to lose. Medea most likely felt as if she had nothing to lose.