that you should never ruin an apology with an excuse.
This one is rather simple and does not require much explanation.
As easy as it may be to excuse yourself from doing any wrong, we all know we make mistakes. There is no need to cover them up. We are human.
But be honest with yourself and those around you. Admit your wrong-doings. Apologize when necessary. A simple "I am sorry" goes a long way, without reasoning. It is easy to explain what may or may not have happened, but it is the apology that means the most, so forget reasons/excuses, keep it simple and if the person wants more information, you can explain, but finish with a simple apology.