How does self awareness help in communication?
The knowledge of ourselves gives us more confidence, as we are a little sure of our reactions to others. For example, if some one in the team is talking about a particular issue, and you know you don't like it, you can manage the situation better either by steering the conversation away, or by avoiding strong comments. If the other person happens to be your client, you can continue the rapport with him/her in spite of having differences of opinion.
Professional communication involves moments where we have to work along with people who think differently from us. Self awareness will give us the ability to control the negotiation with others, keeping passionate emotions in the periphery.
In contemporary democratic political / managerial / organisational setup, non-passionate communication skills are required for the smooth functioning of corporate sectors. The person who is aware of his thoughts will be able to convey ideas with more clarity, keeping in mind that other people think differently.