Possible Digital Signature Hack?
why can't someone generate another private key that will match your
  public key and fool the whole process?


Because in most schemes, this is equivalent to recovering the private key from the public key (this can be somewhat easily seen for RSA and trivially for ECC-based schemes). And as we assume that recovering the private key from the public key is hard, finding a secondary private key that matches a given public key can be considered hard as well.