why is 'sorry' the hardest word?
The answer, I think, is that saying 'sorry' involves a double whammy of painful moral emotion. It essentially involves both guilt and shame. We feel the pain of our guilt in the acknowledgement of our wrongdoing: we 'feel guilty'. And then, when we say 'sorry', we feel the shame of being known for a wrong'un.
Learning to say 'sorry' is a central achievement of such a childhood as goes well enough to produce someone who could be and have a friend. (That remark looks empirical but, given the inevitability of our failing those we love, is basically a 'grammatical' remark on the concept of 'friend'.)
By wronging you I rupture our relationship. (This is true regardless of whether you know what I've done: the relationship is still broken - because it now involves the living of a lie, however unwitting.) By seeking you out and apologising, the possibility of relationship (if you accept my apology) is back on the table.
In order to apologise meaningfully I need a secure enough sense of self. It can't be that the shame I feel utterly undoes me. And having a secure enough sense of self involves trusting that I'm lovable despite my failings.
A good parent coaches and supports the child in the above-described relational repair routine, showing an accepting love at the shameful moment of the child's guilty confession. A poor parent either does not accept apologies - if they continue to hold the wrongdoings against the child, weaponising the acknowledgement of guilt - or brushes them off as if the child hasn't really wronged them - thereby breeding a narcissist.
If you're well-rehearsed in the saying 'sorry' routine, you can benefit in addition from a dignity boon - of knowing that you've (at least now) done the right thing. Rather than holding your head in shame you can, if not quite hold your head up high, at least not be lost in endless self-recriminations. You did wrong; you've tried to put it right; you've owned your bad; and because you're even so a lovable human being, life can go on.