I don’t think this is true at all, though, Samira. People do get forgiven for stuff where they don’t admit fault, all the time. It might be a little harder, but it definitely happens.
For me, forgiveness is usually just a matter of distance and perspective. Stuff starts seeming less and less important as time passes and the larger scheme of things becomes clearer, until pretty soon it feels silly to hold onto ill feelings about some little thing-- and in “the scheme of things,” even big things are pretty little.
Once I start feeling silly holding a grudge, forgiveness comes pretty easily.
I’m sure other people have different approaches, but I don’t think I’m really very unusual in this. Maybe even most people don’t put such a demanding prerequisite on forgiveness as “admit you were wrong.”
Considering how hard it often is for people to admit such a thing, that’s probably for the best.