If someone makes a mistake, an honest apology is a way to own up to that mistake and take responsibility for those actions.

It is also a way to sooth feelings ruffled by your words or actions - whether the impact was intentional or not. If you care about your impact on other people then I would think you would want to apologise where appropriate.

I will be far more likely to interact constructively with someone who has apologised for a 'lapse' than someone who refuses to take responsibility and demonstrates a callous disregard for other peoples' feelings. (Bear in mind that interactions with people with dubious motives fall into another category.)

In recent days, three prominent posters have posted apologies, and this is something that helps make this forum special.