The term self-compassion has been around for around 10-15 years, but the concept is much older than that - it's about being kinder to ourselves. When clients explain their problem to me, it becomes evident very quickly that that's not what it's really about. For example, whilst they may be concerned about lack of confidence, what is even more corrosive and undermining is the way they criticise themselves for not being more confident and assertive, or for blushing when they feel nervous. They will not even give themselves a break, make allowances - so how can they then reasonably expect that from anybody else?
What we're usually looking at is their inability to forgive themselves for being human, imperfect, flawed. Often they will have grown up in a very critical environment, perhaps where adults thought they were doing them a favour by pointing out their mistakes or not allowing them to "get too big for their boots", and they have now taken on the role of fault-finder for themselves, only frequently much harsher.
Others are granted a lot more leeway, treated with greater understanding and kindness, but the self-punishment has to be maintained, because that's the only way they can be good enough to find the approval and love of others. That's how it was in their childhood (except it's probably a fair guess that the goal posts kept moving back then and they never actually found those elusive objectives), that's what they learned about life and love - that nobody could possibly care about them if they discovered the real person underneath. It's the opposite of self-compassion.
The good news is that self-compassion can be learned, and a helpful starting point is to see yourself as a child, or to consider how you may treat a child in similar circumstances. It can take some time and effort to change the habits of a lifetime, you may need help to get there, but it's worth the journey.