When angels appeared to people, why did they begin by saying, "Do not be afraid," as in Matthew 28:5 and in Luke 2:10? I've heard that it was because sometimes people died when they saw angels, but I have no concrete answer. -- Kelsey
I think the angels told them not to fear because it was terrifying to see an angel--assuming you realized it was an angel. Moreover, seeing God nearly always left one weak, breathless, overwhelmed... For example, see Daniel 10:17. What a contrast to the flippant attitude many have today (God is their cosmic buddy!)...
I am unaware of any tradition about people dying on seeing angels... unless you are thinking about the Grim Reaper (the angel of death)!