What are the important points about cryptographic hash functions?

Question

I was reading this question on MD5 hash values and the accepted answer confuses me. One of the main properties, as I understand it, of a cryptopgraphic hash function is tha

Answer 1

Yet the consensus answer to the question "why aren't MD5 hash values reversible?" is because "an infinite number of input strings will generate the same output."

This is true for any hash function, but it is not the essence of a cryptographic hash function.

For short input strings such as passwords it is theoretically possible to reverse a cryptographic hash function, but it ought to be computationally infeasible. I.e. your computation would run too long to be useful.

The reason for this infeasibility is that the input is so thoroughly "mixed together" in the hash value that it becomes impossible to disentangle it with any less effort than the brute force attack of computing the hash value for all inputs