I see a slightly different way to understand this problem (“I can’t make a mistake”).
A few years ago I was watching an animated film when I was unexpectedly shocked by the story.
It was called Lilo & Stitch (ha!, you didn’t expect this one).

There is a moment in the movie when Stitch, the artificially created animal/robot, isolated in an island with a lovely family, builds a small town only to destroy it. That was his purpose. He was programmed to do it.
I related to him.
I felt like I had heard so much that I was bad, that nothing that I ever did was good enough, that whatever horrible thing that happened close to me was my fault and so on, that I understood that I also had been programmed to be a monster. This is something so strong that after my brother and I grew up in a house with an alcoholic father and a N mother and learned to be the most introspective children, we had to listen to our mother saying that she “was afraid of us”. It took me a long time to understand the real consequences of that statement. Today I understand it as she was saying that I was a monster, because my own mother had to be afraid of me (emotional blackmail = don't make waves).
“
He was designed to be a monster.
But now he has nothing to destroy.
You see, I never gave him a greater purpose.
What must it be like to have nothing...
not even memories to visit in the middle of the night?”
Sorry for my long posts, but what I am trying to say is that sometimes we grow up so guilty, so helpless, we carry so many accusations in our minds, that every time we fail, it is like we hear their internalized voices “SEE?!?! I TOLD YOU!!!”
Every time we make the smallest mistake, ALL accusations from a lifetime suddenly seem correct.So maybe it is not exactly that we have to prove that we are perfect. Maybe we are desperately trying to prove they were wrong, that we are not so bad, that we deserve a chance.
“
What happened to your family?
I hear you cry at night.
Do you dream about them?
I know that's why you wreck things and push me.
Our family's little now and we don't have many toys but if you want, you could be part of it.
You could be our baby and we'd raise you to be good.”
We have been fighting to prove this our whole lives. And every single time we fail, it is like they were right. And if they were right it means we are as worthless as they made us feel.
“
I... I...
Lost.
I'm lost.”
So, it might be one of the reasons we/our internal voices are so hard on ourselves when we make mistakes (distorted thinking, I know).
Forgive me for my long posts and ramblings.
Hugs.