Why do are child laws different for children say 13 and a child 16 why arent they both the same ?:
I agree with parts of both of the above answers. It has to do with a childs cognitive development. It is usually during those years children go from concrete to rational thinking. That is why some subjects are not taught until childrem are older.

Some kids on the younger end don't know the difference between right and wrong in many cases. They can have a hard time to know what will happens, or consequence of what they do.  

Sixteen year olds are cognitely far ahead of a child who is 13 in every respect.