Because the surgeon has years of training, to know what's going on. The surgeon has seen hundreds of similar cases, and has gained a lot of experience. The surgeon has a whole team of people to help, and to provide back-up. Confidence comes from having skill. Confidence comes from having at least some of the answers.
Competent people are confident.
Competent people face fearful situations with confidence. Incompetent people, which is how I feel much of the time, have to fall back on courage. Raw courage is when there's nothing you can do, and you can't run away, and you stick it out anyway. Competence is much better. I recommend it.