In the end of the play it is clear to the reader that she does not really want to commit that final act and kill them. Even though she places the blame of her faulty marriage on the boys, they are still her children. She is emotionally attached to them and it affects her to loose them. It despairs her to have to kill them. The real question would be why she felt that she had to kill them. Would it not be enough to simply kill Jason's new wife. To talk his only offspring and leave him alone without anyone to give him more children. This is the question that is most difficult to understand.
At the beginning of the play Medea does not have these same ideas of how to punish Jason. She talks of killing him and destroying his house, but the killing of her children never enters the picture. She seems to believe that the children will have little bearing on the downfall of Jason. It is only after she is banished from Corinth that her mind turns to the idea that for a complete revenge she must kill her children as well. It is almost as if it wasn't until he truly turned from her that this comes to her mind. It was then that she decided to truly turn from him as well and completely destroy his life. At this point in the play Medea turns completely from any sort of morality and hate consumes all of her being. All that she care for is hurting Jason in every possible way. This includes killing her children. At this point hurting him is far more important than anything else could ever be. Even more important than the love and maternity that she feels towards her children.