It seems like a chicken and egg problem.
You can make a write function write to some data store, but never know you saved it properly without a tested read function.
You can make a read function read from a data store, but how do you put stuff in that data store, to read, without a tested write function?
I am connecting to and making transactions with an SQL database to save and load objects for use. There's no point testing the access functions the DB provides, but I wrap such DB functions to serialize/deserialize the objects. I want to be sure I'm writing and reading the right stuff to and from the DB correctly.
It isn't like add/delete, as @snowman mentions. I want to know that the contents I've written are correct, but that requires a well-tested read function. When I read, I want to be sure that my read has correctly created an object equal to what was written; but that requires a well-tested write function.