By relationship I mean state of association between two entities.
Parents, the aged and teachers are givers. They give over chinuch, life experience and wisdom. Children, the young and students receive those things.
The nature of the relationship between a giver and a receiver is that the giver is higher than the receiver. Try to pour from a carton of milk on the floor into the cup on the table.
The nature of the association between a parent and child is that the parent is above the child. By virtue of being ‘higher’, they command respect. That is the nature of respect- it is given to those above us.
If I had to say where the ‘right’ to command respect comes from I would say by virtue of attaining the higher position.