Repeat after me … I failed or I was wrong? … … You’ve failed or you’re wrong? … … He has failed or wrong? … …. ….
There is a difference, perhaps subtle? Between failure and being wrong taken a decision or doing something: both two are “screwing up” but it seems that in the first case, the result is disastrous and the second may still be a solution.
The Cambridge Dictionary defines “failure” as:
1 .- when someone or something does not succeed
As for the word “wrong” (equivalent to “a mistake”) its definition is softer:
1 .- If someone is wrong, they are not correct in their judgment or statement about something
Then, it seems that the dreaded “failure” is somewhat stronger (or at least it sounds) just “a mistake” and yet, we just mixed it and that can be dangerous.