Being an Ambassador for Christ and minister of reconciliation is perhaps the highest level personal interaction possible in life. This means you are encountering souls with the most intimate and penetrating message of their life. Therefore you are asking souls to trust you and listen to what you are saying.
Thus you want your hearers to be able to look you in the eye to see you are sincere, see them as souls who are alive and want them to believe your message.
Plus you want to be able to look into their eyes to see if and how the Spirit is working that you might comment to them directly.
The eyes are the window of souls and you want to be vulnerable and pure enough to have the souls hearing you to be able to look into your souls and connect with you and your message.