God the Son established the Catholic Church because, in part, he established a Church that would be his mystical, visible presence in the world until the end of time. Christians who, for various reasons, lost faith in Christ’s Church established their own churches, thinking (erroneously) that they were doing the will of God.
It should also be said that Christ established the Church itself and gave it a basic hierarchical structure (pope, bishops, priests, deacons) to teach, govern, and sanctify it. But it is incorrect to say that he “establish[ed] the structure, rules, and order of the Catholic Church,” if by that you mean that he micromanaged the creation of the Church down to writing canon law. Much of the Church’s structure, rules, and order is the result of human organizational skill, and not direct inspiration by God.
