It would be a great speculative exercise to wonder where the priest and the Levite where going as they passed someone in such distress. One should have no trouble determining what a priest is. For those who do not know, however, a Levite was one whose tribe members were responsible for attending to things associated with the temple, the worship that took place there and the needs of the priests. Where could they both be going?
Before that is further pursued, the fact that they "passed by on the other side," away from someone who had been injured is of particular note. Certainly tradition holds that this took place on a road that was frequented by robbers. Perhaps they were both concerned about their own safety and decided to give the situation a wide berth.
Suppose they were just in a hurry. Suppose they were in a hurry because they were late. Suppose they were in a hurry because they were late for a temple worship or class. Suppose they were in a hurry because they were late for a temple worship or class where they were scheduled to discuss how to treat one's fellow man. Just suppose.
Beloved, Christianity is not a claim, it is a calling. It is not for show but for shouldering. It is not just for hearing but for helping. It is not just for believing but being. I wonder how often we pass up the opportunity to do good on the way to "church"...where we are told to do good.
Faith without works is dead.