Jor-El gave his son an epic charge: be their protector. Here is an alien with God-like powers that has charged himself with protecting his adopted planet. People will be afraid. Governments will hate him. Nefarious characters will try to use him. Once he is accepted, how long before people rely on him too much? Can Superman be everywhere at once? How long before they resent him? How does he choose between his own life and his charge?
Jor El, warned him of this in the first movie...
Jor-El: You are revealed to the world. Very well, so be it. But you must still retain your secret identity.
Superman: But why?
Jor-El: The reasons are two. First, you cannot serve humanity twenty-eight hours a day.
Jor-El: Or twenty-four, as it is in Earth time. Your help would be called for endlessly, even for those problems which human beings could solve themselves. It is their habit to abuse their resources in such a way.
Superman: And, second?
Jor-El: Second, your enemies will discover that the only way to hurt you, will be by hurting the people you care for.
Superman: Thank you, Father.
Jor-El: Lastly... Do not punish yourself for your feelings of vanity. Simply learn to control them. It is an affliction common to all, even on Krypton. Our destruction could have been avoided had it not been for the vanity of some who considered us indestructible. Were it not for vanity, why... at this very moment...