Why unhashing is not possible?

I've always led the belief that if something can be created/built,
then it can be "uncreated/unbuilt". In technology this is sometimes
referred to as reverse-engineering. I understand too how hashing can
be used within programs and fast database lookups but I failed
miserably discussing the subject of hashes with someone who could not
understand when I told them that you cannot reverse the process... I
know you can crudely hack it (using John the Ripper for example) but
you cannot "uncompress it" so to speak.

So... my question here to you good people is... why can't a hash be...
well... unhashed?

Surely if the hash is unique, we know the process that got us the hash
we have only to reverse the process... we can't... so... but why not?
.

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