First off, it's disabling the basic principal behind an apology: self-accountability or integrity. By this 'thinking' an simple "I'm Sorry" is an get out of jail free card and the reasons needing to actually own up to one's own stupidity is irrelevant, just smooth it over with the magic phrase. Right? Only if you live in a world where your shit smells like flowers and every cat stops to kowtow to you as you pass. Since cats tend to think they're deities and not the other way around - this is a bounced reality check.
If one really do care of the person one's in a relationship with - whether just friends or more - this is a slap in the face demeaning. The apology's just empty words in this context with no need to express regret, admittance of being in the wrong, and quite frankly expresses how little one thinks of the person and the actual relationship. It would be more honest to come on out and admit to using the person for whatever means!
The second phase in this 'gem': "it means that your relationship is valuable than your ego" probably should have been written "It means that your relationship is more valuable than your ego." It makes more sense and also unhealthy! Talk about a two-fer spiel, eh?
Yes, a sense of self is very healthy - after all a person is more than the relationships they have! A poor ego often denotes a poor self-esteem, and if one cannot love themselves they are incapable of loving others due to the clot of self-loathing or hatred. Often this mixture leaves a person in a very dire jeopardy of abuse which an unhealthy ego will try to fix an internal problem with an external one!
Domestic abuse and other toxic relationships often stem from those who will sacrifice their egos to be in a relationship with someone who in truth, is most likely is the least deserving person. Yes, I did go there - a person who only tears down someone they supposedly 'love' or 'care about' repeatedly is not worthy of being in a relationship for they truly are about control. They lack self-discipline most of the time and like the one often abused by them, they seek external solutions to an internal one.
Abuse often has the lack of integrity - the abused and abuser both will blame anything/anyone but the one responsible! It is not acceptable to have someone to get a beat down because they didn't do everything as the abuser wanted, it's not the abused responsibility to make the abuser happy either. They both need to realize that they alone are accountable for their own actions - and not the other person.
So in closing, apologize when you do something wrong - if it's not your bad don't apologize. Realize you are the one that is in control of yourself, which also means owning up to one's own choices - the good, the bad, and the ugly - no one else. Relationships work well when the other person is treasured as well as you treasure yourself - it's how I have stayed happily married for fifteen years with the man I love!