Tell us why some people will never say that I am sorry, even when it is obvious that they are wrong:

This type of reaction as a form of pride or stubbornness, however, this inability often hides deeper motives. When a person shows difficulties in saying sorry or in recognizing their part of error or responsibility, what happens is that they are actually deploying a series of efforts to protect a fragile perception of their own "I". Thus, for some, saying "I'm sorry" has psychological repercussions that go far beyond what these two words mean initially. They awaken in them deep fears - both conscious and unconscious - that live as a threat to their person. Hence, try desperately to avoid apology. We know that admitting your mistakes can be hard on the ego,
but if you see it from a selfish point of view, there is additional incentive to do it beyond helping the other person feel good again.

How do we handle friends or people who will never say they feel it?

Saying sorry is something threatening for a person who does not apologize, they have problems separating their actions from their personality. For example, if they did something wrong it is because they must be bad people; Therefore, saying sorry is a great threat to your basic sense of identity and self-esteem. For those who will never say sorry, it can open the door of shame; what makes you feel bad about yourself, if you are one of the people who do not apologize or ask for forgiveness, begins to ask you if you would not feel better by saying a simple "I'm sorry"; this single phrase can save you from breaking relationships with a loved one.
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What is the importance of saying "I'm sorry"?

The important thing here is to use that word with love, respect and responsibility, to have the humility to pronounce it when we have made a mistake and to show affection in that way. Sometimes people who are upset with you just need you to acknowledge your mistake, simply show that the other person really cares about you.