To own something means “belonging to oneself or itself—usually used following a possessive case or possessive adjective <cooked my own dinner>.” 1
Owning the mistake means that the wrongness belongs to you instead of to an experience based upon a decision made that lacked clarity or wisdom. Once you own the error, it then belongs to you. It remains in your possession and the law of ownership binds it. Now you will have to figure out how to dispose of it.
Do you put it in your garage? Or your attic? Do you put it in your storage unit? Do you donate it? Maybe you can try to sell it, cheaply, at a garage sale! But somehow I don’t think that anyone would want to purchase anyone else’s mistakes, or want them even if they were free.
The most pragmatic solution when a mistake is made is to learn from it, pray to forgive yourself, and then let it go so you can move on freely.
Holding on to the blunder or claiming it as a possession will increase the weight of the burden. It will grow heavier over time as more mistakes are made, because I doubt very much that only one mistake per person is made. The burden can become unbearable.
My mentor explained to me that life is a lesson and an exercise. So, if we are here to learn and to grow stronger, then owning a mistake may extend the grief, the embarrassment, and the shame of making it in the first place.
George Bernard Shaw said, “A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.”
So own the honor of humility and allow yourself to be humbled by the error rather than burdened by it.