A sincere apology has three parts:
1. I am sorry
2. It is my fault
3. what can I do to make it right?
Normally people have own pride, so even people made some mistake,
they do not want to express their apology, but excuse and making some reasons,
in order to protect their self.
We are all human being, so we would make mistake somehow,
So each moments it would be better to express apology
accepting what we made mistake.
It is hardest things that drop our pride and accept our mistake,
but in this way, we can be honest ourselves, and
not to tell a lie for ourselves.
The things which you made mistake, and not telling any apology,
even we can deceive someone,
but we cannot deceive our conscience.
The Apology is very important for both of us
for the others and for ourselves.
Be brave and express apology,
You would feel better when you say sorry sincerely.