In reality, apologizing is a sign of strength. It takes courage to say "I'm sorry, I messed up, I didn't mean to, I sincerely apolgize for this".
It shows that:
you don't make excuses,
you take responsibility for your actions,
you don't pretend to know it all and are willing to question yourself,
you respect the person and their feelings,
therefore you respect yourself
you are human, we all are, and it's ok