How come MD5 hash values are not reversible?

The input material can be an infinite length, where the output is always 128 bits long. This means that an infinite number of input strings will generate the same output.

If you pick a random number and divide it by 2 but only write down the remainder, you'll get either a 0 or 1 -- even or odd, respectively. Is it possible to take that 0 or 1 and get the original number?

If hash functions such as MD5 were reversible then it would have been a watershed event in the history of data compression algorithms! Its easy to see that if MD5 were reversible then arbitrary chunks of data of arbitrary size could be represented by a mere 128 bits without any loss of information. Thus you would have been able to reconstruct the original message from a 128 bit number regardless of the size of the original message.