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Encryption is a two-way function; what is encrypted can be decrypted with the proper key. Hashing, however, is a one-way function that scrambles plain text to produce a unique message digest. With a properly designed algorithm, there is no way to reverse the hashing process to reveal the original password.
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The only purpose cryptographic hash functions serve is to compare two pieces of data, such as when downloading files, storing passwords, and pulling data from a database. It's possible for a cryptographic hash function to produce the same checksum for different pieces of data.
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As usual, you're using doubletalk and skewing definitions to cover your incompetence in this area. The gist of the discussion is about long processes that can be quickly checked. Reversible
cryptographic hashing would not entail a long process, by which to contrast quantum computing to what we have today; therefore, we must have been referencing proper hashing. Reading comprehension tw, I haz it - you don't. You really need to learn stuff before posting your feelings so you understand what people are talking about.