why do the kids always jump in instead of dive in?

Your child’s safety is a primary concern of your coach and USA Swimming.  By jumping in feet first, your child is considerably reducing his chance of being injured.  Although accidents are very rare in swimming, injuries do occur.  The practice of jumping, rather than diving, is simply a safety precaution and a safety policy of USA Swimming.

why the kids aren't allowed to go off the diving boards?

Diving off the boards is not an insured activity and thus is prohibited by USA Swimming.  Once again your child’s coach and USA Swimming are concerned with your child’s safety.  Your coach and swim club are not covered by the USA Swimming’s insurance if a child is injured while going off the boards.  Although going off the board is fun; it is not worth the risk of exposing your child to injury and your club to liability.