The greeting of salām is an act of kindness, not a contest for rank. People can initiate it with relatives, neighbors, colleagues and fellow learners in a respectful manner.
If two people have become distant after a misunderstanding, the one who first greets the other need not be confessing to a wrong they did not commit. They may simply be reopening the door to courtesy.
Humility does not mean accepting injustice: a person can initiate salām and still address a real grievance calmly and fairly.