Apologizing is an important act of personal accountability and responsibility.
Someone who is capable of looking within, take responsibility, and resolve conflict directly is a sign of a healthy person.
Being capable to take duty for our affect on other people, admit and own our errors and defects, creates restore trust and connection especially with the people close to us. These are all important aspects of living an accomplished life and creating healthy relationships.
At the same time, we can devaluate, contempt, and do harm to ourselves and those around us, by apologizing for who we are in a shame-based way – which generally comes by a place of shame (feeling as if we're not good enough or there's something inherently wrong with us) or guilt.
Apologizing genuinely is about accepting responsibility for our actions, our affect, or our responses that.
Apologizing for who we are is very much about us thinking or saying some adaptation of, "I'm bad, it's my fault, or do not hate me," like we are a baby looking for establishment or approval.