Detachment is detaching yourself from identifying with yourself as body, mind or spirit. Many people suppress their emotions. To suppress your emotions is just as bad as indulging your emotions. What you have to learn to do is to look at your emotions and not indulge them and not suppress them either. It is like creating a space between you and them.
Most people immediately identify with their emotion, whatever it is.
They have done so all their lives and so they take it for granted. They feel every negative emotion and they think it is their right to experience them. The point is you have to be detached, not by detaching from life but to be very aware, to look very seriously at what is happening but not to identify with it. But it takes just a little space to create a bigger space. The best way I can think of is to study Krishnamurti.