People are often interested in creating relationships based on equality. For horse--people relationships, this approach is dangerous. Horses must always be subordinate to their riders.
Leadership however, is not about control. Leadership is about helping the horse understand that under almost all conditions that the human handler knows what to do. It's like a dance. Someone has to lead. Otherwise toes get stepped on and one or both of the dancers is likely to end up on the ground.
When the horse is convinced that human is in charge (and not controlling), they will listen more to you than worry about what is happening all around them.