Many people are afraid of horses. Some just have specific hang-ups while they are riding. Many of my students wish to overcome these fears. I had a serious accident on a horse eleven years ago that shook me to my core and left a metal plate in my arm. Over time, I had to rebuild my own confidence so that I could ride again without the the fear of falling overtaking me.
I will never push my students beyond their capabilities nor encourage them to do anything out of their comfort zone. While I believe everyone can overcome their concerns in time, I also believe it should be done carefully, softly, and with as much time as needed to progress. If I see that a student is ready for a new challenge, to ensure comfort zones, I will often wait a lesson or two before introducing new concepts. This results in slow and steady growth in all areas of riding skills.