I think it shows integrity and strong character, it also clears things up and brings peace. I have no problem apologising because I'm not perfect, and none of us are, and no ones infallible. I find that if you admit fault, or that you are far from perfect it makes you more approachable and it builds bonds, whereas being too proud to apologise or admit imperfections builds suspicion, defensiveness and distrust. Apologising requires humility and that is always an attractive trait because it builds bridges, being too proud to apologise builds animosity.