First of all, the mental part of coaching someone in athletics, life or whatever is difficult. Every person is different and responds differently to coaching. Some people you can raise your voice at and they take the hint, others (probably most) will perform worse after getting yelled at. In running some people like to know the day to day detailed schedule weeks in advance and others like to know it just minutes before they do it because if they know about it ahead of time they will over think the work and tell themselves it is too hard and they can't do it.
Now the goal of coaching is to convince someone that he or she can reach a goal. That is it. Often a coach is a resource who can act as a facilitator, teacher, guide, positive authority figure, friend, and leader, but not necessarily. About that last one, leader, I have been on enough disgruntled teams to know that while everyone shows up and does the workouts the coach may not be an effective leader.
I used the word convince, not achieve, because the coach is not there to ensure you get to that level. The coach is there to help you get to that level. If we achieved our goals every time our goals are too easy or we are amazing.
A few mental tips to make race day go easier: triple knot your shoes (I've had doubles come undone), make a race plan at least the day before so you don't have to worry about it that morning, stick to the race plan, have confidence in your training so that when someone tries to pass you, you know you can hold them off, and don't forget to have fun!