The point of the question is to see how you address challenges and difficulties. It also gets at how you think about yourself, areas you want to grow in. They want to know if you have actually given to thought to the concept that you won’t always succeed, that you will make mistakes, and that you have continued growth in front of you.
As an employer, I really want to know if you are capable of learning and developing. I want to know if you have the habit self-examination, if you have perspective on yourself, and if you have confidence in yourself. That last one is interesting, because I don’t want to work with someone who beats up on themselves. Lack of confidence and anxiety are really hard to deal with in a coworker or staff person. The person who is able to see that they are not strong in every area is a confident person. The assumption is that you’re good in some areas.
No one is good at everything. Are you aware of that? And how have you compensated for that?
I suggest rephrasing your answer in this way:
“I’ve have learned about myself that I have a challenge in xyz. I have learned to compensate for this by doing abc.”
For example, “I have a challenge in managing multiple tasks for my boss. I want to do all of them at the same time which is impossible. And sometimes my boss wants something that I didn’t realize was the top priority. So I’ve learned to ask for clarity in terms of what is the top priority. I’ve also learned that communication is really important, to let my boss know what I’m working on and to provide regular status reports, whether they ask for it or not. I realize I don’t have to manage it all myself. I also now use lists all the time so I don’t keep things in my head and I can visually see what I have to do by when.”
You demonstrate self-knowledge and the capacity to learn. That’s what most employers want from someone.
So always rephrase the weakness question or the failure question or mistake question as if you used it as a learning experience, a chance to solve a work-related problem, and an opportunity to grow and therefore add more value to the company or organization.