The answer without lengthy mathematical formulas to the essential part of your question which is about reverse engineering a private key from a public key is presented here:
A private key cannot be (easily) mathematically generated from a public key (i.e. "one-way function")
Specifically in case of elliptic-curve cryptography, the one-way function is discrete exponential and logarithm (and not a trapdoor mentioned in the referenced original answer which is used by the RSA algorithm).