This is a flaw in your assumptions. It is not one directional. The private and public keys are two parts of a puzzle. The puzzle is easy to make but so hard to solve that it is effectively impossible. However there is one exception. There is a shortcut that makes the solving very fast and easy. There is a secret "trap door" that enables bypassing of the impossibly hard route and to open it you need  the right [private] key.

So one gives the public key to anyone that wishes to make a puzzle. Once created only the person that knows the key to the "trap door" can solve it. This is why they are termed "key pairs" since a private and public key are related by the "trap door".

This is the premise behind most cryptography that is based on a "trap door function" and includes Elliptic Curve, RSA and DSA to name the more common ones.

Hopefully you can see that to tell everyone how to open the secret trap door is, in general, not a good idea.