When you apologize, it says:
- I’m sorry
- I accept the blame
- I’m responsible for everything that went wrong here
- I’m the only person that was guilty here, forget about others
- You can remember that this was my fault
An honest apology, when needed, is good practice. Apologize too often and take on the responsability. Your name will be remembered with the issue and your reputation will take a hit.
Don’t apologize if you don’t have to. It focuses guilt, attention and responsability and make you appear worst than you actually were.