We're asked to demonstrate that nothing our brother does has the ability to affect us.
We're asked to show by example that our brother has no ability to hurt us or harm us or upset us or offend us.
If we demonstrate this, we are showing the truth to our brother who, if they are attempting to do something to cause us to be upset, must be mistaken about what the truth is. Truth cannot be attacked and attempting to do so is utterly wasted.
This demonstration shows them what the truth is, by demonstrating that the True Self is beyond the reach of all ego attacks and all ways that the ego targets individuals.
What cannot be affected by the world reveals that what our brother does has no effects. This proves to them that regardless of what they think they did, even if they did it seemingly intentionally, it has had no effects at all and so did not happen.
This is a demonstration that they did not really sin, or that whatever sin they seemed to do had no power to do anything to anyone. This literally requires complete invulnerability and demonstrates immortality.
If you can be sick or upset or offended or hurt by anyone or anything, you are demonstrating that you are less than immortal. "Sickness is an attempt to demonstrate that you can be hurt". - ACIM
If you cannot be hurt and are not hurt because you realize that you can only hurt yourself and you stop doing so, then nothing anyone attempts to do can hurt you. If their attempts to hurt you fails, or in other words, their attempts to sin do not produce any effects, this proves to them that sin can be undone and that nothing has happened.
This demonstration of innocence proves their innocence as well as your own. It teaches that forgiveness is called for and is present and is given, and that whatever they thought they did or whatever reason they seemed to have for doing it, it is completely irrelevant and nonsense and false and unreal.
This educates your brother that they are innocent in spite of what they think they did, which may be shocking to them but it will set them free. It will heal their mind and show them that what they believe about themselves cannot be true. They do not have the power to affect the Son of God. They do not have the power to destroy God's Creation. They have no authority over Christ and who they thought they were is not who they must be.
Be a living demonstration that this is your complete, whole truth, at all times, in order to be the salvation of the world. If you choose to go into upset and offense and reactions and fear and suffering, you are failing to fulfill this function and are in denial about who and what you really are. You are not being true to yourself. Only by being true to yourself can you be the truth to others.
You are not saving the world when you are offended by what other people do and feel hurt by it and react based on that, even if it is with good intentions or an attempt to help. You are not the salvation of the world if you keep attacking yourself and hurting yourself and then are accusing others of putting this hurt into you and are using that to justify retaliation or judgement. You are not anyone's savior if you are upset by anything anyone does or says or attempts to make happen.
These are all false attempts at salvation, designed to make it look like you care and want to save the world from suffering, but is really an attack. It is an attack on yourself and on the other person when you take their attempted attack seriously, fail to overlook it, and fail to demonstrate that it is meaningless. When you take it seriously and react to it and then try to fight with it to stop it, you are delusional and are fighting with your own self-attacking perceptions. This isn't helping anyone. It is the ego's version of salvation and is a complete lie.
You are the salvation of the world only when you demonstrate that the world IS saved from attack because attack is impossible. You are the salvation of the world only when you demonstrate that there has been no sin, can be no sin, sin has no effects, everyone is equally innocent, and God loves everyone just the same. You are only a savior when you are able to show that you are unharmed, unharmable, harmless and cannot be harming to others, because regardless of what transpires, it does not change you whatsoever.
You are immortal. You are the light of the world. You only function is salvation.