A sincere apology is not given to feel less guilt for yourself, it is given because you understand how and why you have hurt the other person.
Apologising whilst explaining how you have caused harm to the other person shows you are fully aware. If you say “sorry” with nothing behind it then it’s not sincere, it’s lip service.
Excuses do not matter, do not even bring them up. If you are truly sorry you know that an excuse does not take away from the hurt you have caused.
If the person wants to continue the friendship/relationship (whatever capacity it may be) then do some introspection and ensure your behaviour reflects that you have learnt from it and are putting that learning into practice. If you continue to be a dick then apologising was meaningless.
We all fuck up, we all make mistakes because we are human.
Just to add, forgiveness doesn’t need an apology because forgiveness is for the person who has been hurt. When we hold on to hate or anger we are giving energy to something not worth our time. It’s also not easy in a lot of cases but when you reach that point it is incredibly beneficial.