Greetings, this is my entrance.
Answer No. 1
It can be for the parenting obtained either from their parents or relatives in which, traditionally, they do not recognize their mistakes or failures, either because of their ego or lack of humility and they think that by doing so they are humiliating themselves.
Answer No. 2
To these people we must make them see that the phrase "I'm sorry" is a magic word, through it we can rectify our mistakes and with that they are not humiliating themselves. Nor is it that with saying it they will feel less than other people. You have to make them see the meaning of this phrase.
Answer No. 3
It is important to say "I'm sorry" this allows us to be good with oneself and with others since with this phrase we recognize mistakes and allow us to rectify and demonstrate to them humility and equality.
Thanks @kweenbrand for the opportunity to participate, greetings from Venezuela.