Fathers and Sons

After their last run through the snow, Eliezer and his father meet up with a kind man named Rabbi Eliahou. The Rabbi is looking for his son, and Eliezer lies to the older man. During the run, Eliezer saw the other boy abandon his father, but Eliezer does not tell the Rabbi this. Why does Eliezer think the other boy left his father? Why doesn't Eliezer share this information?