(someone) owes (someone) an apology

"I owe you an apology" means "I think I should apologize to you." You say this when you realize that you did something wrong, and you want to say that you're sorry.

You can also say this to other people if they've done something wrong. For example, you can say this to a child who took a toy from another child:

Kai, I think you owe Nelly an apology.

It was wrong of (someone) to (do something).

Use this phrase when someone has done something that they shouldn't have done:

It was wrong of me to doubt you.

It was wrong of him to say that.

Most often, we use this phrase when someone has hurt another person's feelings.

You wouldn't use "It was wrong of ___" if someone broke a rule or law. For example, it would sound strange to use this phrase to talk about a man who hit his wife.