It is aggressive but in a positive sense. It shows that you are listening, you are not afraid and got confidence. If you are not afraid and got confidence, it shows that you can handle the situation and that you are the person your client is looking for.
There is a difference between looking in the eyes and staring at someone in the eyes. It is okay to look away from time to time at the stuff you are talking about. Looking too much in the eyes becomes starring and that is creepy.
Communication is important in business. Good communication is efficient work. If you know how to communicate is a positiv way, you have leadership. Leadership is not just about yelling at your employees to do this and that, leadership is how you handle things efficiently and how good you communicate with others in a positive way.
EDIT: I didn't read Legga's post before writing that, but yes, Legga is right. Try focusing on the face if the eyes intimidates you, between the eyes is a good spot (you don't directly look into the eyes and the other person think you are). Try relaxing a bit before the meeting or the phone call. Try to laugh a bit about the situation.