Monty Roberts makes the argument that looking a horse in the eye drives him away, that it is interpreted by the horse as a challenge.
I don't want you to think you can never look your horse in the eye, so let me add my thoughts to this. I believe what Monty is talking about is a hard, focused stare. This could be read by the horse as assertive body language and could easily make him uncomfortable.
A soft gaze is a different matter and may even tend to calm your horse if it is also reflected in the rest of your body. This is especially true if you have established a strong relationship with the horse and he trusts you.
Remember, horses read our intentions by reading our bodies. Keep your thoughts positive and supportive and things will usually go better.