Hate to be the one to tell you, but the authority of having kids gives some of you an ugly god complex. You want a strong foundation? You want your respect back? You wanna move forward? Show integrity first hand. So often parents drag the passage in the Bible that tells children to obey the parents and skip the part that says not to exasperate them or discourage them…
For too many, apologies mean admitting they had a role in the issue, they they could have been wrong (even if they actually were) apologizing is seen as weak, inadequate and adults REFUSE to be wrong in the eyes of a child.
“I’m sorry you carried this so long, alone”
“Im sorry I told you to live YOUR life, MY way”
“I’m sorry you felt that you couldn’t come to me”
“I’m sorry I took away your chance to grow by constantly reminding you “you not grown””
“I’m sorry I chose not to listen to you solely because I saw you as a child”
“I’m sorry this was the best life that I could give you”
“I’m sorry I wanted more from you, making you feel that your efforts weren’t enough”
“I’m sorry I didn’t lead by example”
“I’m sorry I didn’t believe you”
“Im sorry I chose not to listen to you”
“I’m sorry for putting you in that situation even when I knew you were uncomfortable ”
“I’m sorry that I’ve shaped you into a broken adult”
“I’m sorry I said “but” invalidating the apology.”
“I’m sorry I didn’t accept the way you tried to communicate with me”
“I’m sorry the bad parenting I received was the example I raised you on”
“I’m sorry for taking away the safe space for you to show emotion”
“I’m sorry I judged you, compared you, scolded you, for being you”.
“I’m sorry the best advice I had at the time was “you need to grow up” with no example of what to grow into”
“I’m sorry for leading you to believe I could honor promises that I’ve broken”
“I’m sorry you had to worry as a child the things I were to cover”
“I’m sorry the only resources I gave you were opposite of what you wanted for your life”
“I’m sorry that I have to play a role in the healing you need now”
You Forgot Your Common Sense 
Some parents just want their best to their child so they do apologize if something’s wrong but some children want to be left alone and want nothing from their parents and want to do only whatever they want..so it’s really how you treat them and grow but parents should apologize ONLY they are the wrong