It is easy to give advice to others about forgiving when somebody apologizes to them, but only the person who has suffered can decide if the apology qualifies for forgiveness at all.
It's not an apology, when the word 'sorry' comes from mouth, not from heart.
It's not an apology, when you proclaim yourself to be right and still say sorry for the sake of ending/dismissing the argument/discussion.
It's not an apology, when you say sorry with expectation of forgiveness and then goes on to complain that the other person is petty and unforgiving.
It's not an apology, when you say sorry to demean the other person and their grievances as unreasonable and childish.
It's not an apology, when you think you are doing a favour on the other person by saying sorry.
It's not an apology, when you neither acknowledge your mistake nor regret your actions.
It's an apology, when you recognise the wrongs you have done or hurts you have caused.
It's an apology, when you don't understand your mistake, but willing to discuss your point atleast once.
It's an apology, when your understand that mere sorry won't undo the pain and suffering.
It's an apology, when you regret your actions and is willing to improve your behaviour.
It's an apology, when you still feel remorse, even if the other is not ready to forgive.
It's an apology, when you genuinely say sorry and not with purpose of putting a display of your magnamity and wise nature.
Maturity is when you understand that every person deserve a second chance, but only when he actually repents for his mistake and seek forgiveness from heart. If apology does not come from within, then it is certainty that mistake will be repeated. Then both the person forgiving and person seeking forgiveness, would be trapped in a cycle of toxicity.
And never apologize when you know in your heart you are not wrong. People might call it showing maturity and saving relationship, but it is just a stopgap measure, which won't improve anything in the long run if the other person continues the same behaviour.