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​The older I get the more I realize how fallible I am.  That in itself is an eye opener.  I appreciate it may be unbelievable to some, but it is true.
When I was younger, I still tried to be nice with people but deep down it was like I knew best.  What I held to, at best may have been an incomplete picture, and at worst plain wrong.  I may have been sincerely wrong but no matter what word I put in front of wrong, wrong is still wrong.
Teenagers are notorious for knowing everything.  They love to roll their eyes saying but not in words, “what would you know.  You may think you know but you do not because I know everything.”
What can be really bad for me is being part right and mostly wrong.  The 20% right part can be really attractive.  But what goes with it is not.
What matters most to me is a willingness to change positions in the light of new information.  Unfortunately, some are not.  What does not align with what is believed is seen as either a lie or undergoes a transformation to fit within the current belief system.
It is by working through something I get to see the error of my ways.  I am not a fan of the reward structure for our current maths system, but I do see the sense in seeing where someone went wrong, and correcting it for next time.
We changed our table tennis points system similar to that.  Previously a person either won or lost.  The team that won got a one and the team that lost got a zero and the person who lost got zero.  We still have the team getting either a one or zero, but we also have a reward for the individuals result.  Someone who loses three zero still gets nothing, but someone who loses three two has their personal effort acknowledged by rewarding them for the two games they won.
But the team still lost that match.  The team still gets zero for that match.  Even if they lost 16/14 in the fifth set of the match.  They lost.  Close is still a loss.  If I got the point every time I was close I reckon I would be right up there.  But a one millimetre miss is the same as a 150 mm miss.  It is still a miss and the other person gets the point.
What I hold to can be like within one millimetre of being right, but it is still wrong.  I may as well be 150 mm away because close is still wrong and the consequence is the same.
I have done a bit of table tennis coaching in my time and like to watch players play.  Often beginners do everything right but still hit the ball into the net or long.  I really do not mind as I know if they are doing it right, they will get it right.  A slight adjustment turns a close into a winner.