What is it about a vasectomy that makes most men shy away from having the procedure done?

Fear. Most men prize their "equipment" and are afraid of "being snipped" because it might damage their prized equipment. It is mildly painful, but buys the guy a lot of less fear of an unwanted pregnancy. Some men feel that they aren't "real "med" unless they can cause a pregnancy, a neanderthal concept.
Vasectomy. Men need to understand that vasectomy will not affect sex, erection, ejaculation. Testosterone level is not affected. It take 10-15 min, so quick it is not painful. He'll be walking out of office and no one will know what happened. He will be sorry he did not do it earlier. Is that simple.