An apology comes down to an agreement between two people about an event. When those two people are a different gender, involved in a relationship, it gets complicated as you describe.
The person who caused the error or discourtesy may decide to accept responsibility. It may not be obvious to the offender at first. It's up to offender to offer some form of regret. This is where it gets complicated. The person who gets harmed as in your story has to feel harmed. The person who accepts responsibility for harm should apologize in a timely fashion. The apology has to be heard as sincere. The hearer may or may not forgive the person causing harm. Or wait to forgive the person to emphasize the seriousness of the error. It's hard to generalize, but women wait longer to forgive than men. And generally men see harm as less serious.