This is a common feature of mathematics; doing many things is much easier in one direction than the reverse. Encryption systems are built on this idea, e.g. RS

This is a common feature of mathematics; doing many things is much easier in one direction than the reverse. Encryption systems are built on this idea, e.g. RSA relies on multiplication of large integers being very easy and factoring large integers being very hard. That doesn't really answer your question - I'm not sure there is a clear reason.