> in general a hash code contains less information
That is true, but has nothing to do with your ability to use a rainbow table or dictionary attack on my hashed statement.
The specific reason why you can reverse my hash is because it's unsalted. The time-complexity of my example hash is somewhat low.
'you are wrong' is 13 characters that spans the lowercase alphabet with spaces, in all english words that can be found in a dictionary. The actual key-space is 13^10 because of the limited characters I used, but when creating a rainbow-table it would probably take a key-space of 13^27 because you don't know the specific characters I'm using. (There are 13 characters in my statement, then there are 26 lower-case letters in the alphabet - plus space - which makes 27... 13^27)
Now, if I followed general op-sec suggestions I would have added a salt to my statement, so the process looks like SHA512('you are wrong' + '7aomAxgeVjAvyDXGrdmNJNKuuiumYbkG') which gives you the possible key-space of 45^63. Also, the salt should be something not found in a dictionary.
On the upper-side of the estimate there are 10^82 atoms in the universe. There are about 14^103 possible solutions to that salted hash above, with many possible collisions. Good luck with creating a database that needs more rows than available atoms, or waiting for a brute-force to complete on that hash, then sorting through the collisions. This is the "impossible" reversible hash you are talking about.
If you are interested in this topic and would like to do this in your code: use the HMAC function which is built for this, or specifically for passwords use bcrypt/blowfish because that algorithm is designed to run slowly (brute force protection).
