I agree with much of what is written here except for labelling emotions as positive or negative.
For me a much better term is "appropriate emotions", whether we are naming and managing them in ourselves or trying to manage emotions in others.
Harnessing the power of the right emotion at the right time can be incredibly powerful when we are trying to influence others. In these circumstances all emotions can be positive, or if used badly, negative.
Ultimately, negative emotions play an important and healthy role in how we understand and react to the world. Guilt and shame are essential to a sense of morality. Anger is a legitimate response to injustice. Sadness helps us process tragedy. And happiness is great too. Just not all the time.