Perception of apologies varies from one individual to the next, based mainly on childhood experiences.
Many people believe that to give an apology is to accept blame and to make an admission of having made a mistake or error of judgement. Such individuals give apologies rarely, and when they do, it is early in a conflict where objective facts make it difficult for them to deny culpability.
Others believe an apology is an expression of emotional acceptance and understanding of the (possibly minor or unavoidable) role they played in the misfortunes of another. These people will give an apology when their actions have hurt another person or a community even though they believe their actions were appropriate. The harm may have been inadvertent or may have been unavoidable.
Still others will offer an apology or expression of sorrow to show that they share, at an emotional level, care, sympathy and concern for the hurt person or community. Such an expression of sympathy has nothing to do with culpability whatsoever.
With such widely varying views of the nature and content of apologies, it is unsurprising that conflicts occur about the need to apologize and the sincerity of any apologies tendered.
As noted above, apologies are sometimes demanded as a closing gambit in a conflict. The demand is made by those who perceive themselves to be in a position of greater power, and is often a precondition for reconciliation steps of some kind. There are two main motivations. One is to gain a tacit acknowledgement of the power one party has over the other. The other is to force the weaker party to accept responsibility for the conflict in the hope of preventing a repeat occurence.
The result of demanding an apology is uniformly poor.
In most cases, a shared view of the power structure does not exist. A person who accepts that they are in a weaker position is unlikely to push matters so far that the more powerful side demands an apology. With the tables turned, a person or community that accepts its weakness is unlikely to demand an apology of anyone. Thus, the demand for an apology refocuses the conflict on a) past issues, and b) the power balance.
There are two usual outcomes. Most frequently, the party asked to apologize will engage in activities designed to demonstrate their power and the rightness of their past actions. This may range from exercising a silent RightToLeave, content removal as with a WikiMindWipe, or deliberate attempts to undermine the project through vandalism, trolling, a fork, or other means. There may be some lobbying of other members of the community in an attempt to validate and exercise the degree of power they hold.
The less common outcome is an effort to manipulate the situation. This usually takes the form of a partial apology or an apology followed immediately by contradictory or inflammatory statements or actions. The party who demanded the apology then faces a paradox: accepting the apology means that the previously withheld "carrot" -- continued participation in the community in most cases -- must be released. Denying the sincerity of the apology, even if justified, is likely to split the community and outside observers, and lead to charges of unfairness.
In short, demanding an apology is a failure to ControlYourself. Rather, it is an attempt to control the other party.
Don't demand apologies. To demonstrate power, DissuadeReputation is more effective. In conversing with a previously problematic contributor, focus on the future. Ask what the contributor plans to do during participation. Ask questions about hypothetical "what if" scenarios, and see whether the response is measured or vitriolic. TimeHealsAllWounds so allow some time apart for the charge to drain away.
This is not to deny the power that sincere apologies can have as part of a wider process of rebuilding trust and mutual confidence. However, to be effective in this way, apologies must be freely given, not demanded or extorted.