Why children draw without a nose?

Most children tend to draw in very basic forms... a big circle for a head, little circles for eyes, a curve for the mouth etc. Noses are pretty difficult to render simply. so it is easier just to not draw them at all.
As the child's ability to observe their subject increases their drawing gain sophistication and details. The only other thing that might influence them is if there is someone in their sphere of knowledge who draws well. An artist in the family tends to speed up the process considerably.