Why can't hashing be used to securely store data that needs to be accessed in its original form?

Hashing uses a one-way function and should not be able to be reversed. This means that you can use hashing to securely store a password because you can hash the password, then compare hashes without needing to know the password. If you hash a database field, however, there's no way to know what the original data was from the hash. Hashing should not be reversible, and it does not use symmetric or asymmetric encryption.