Having gone from quite insecure to very secure over the years, I would like to disagree. Admitting that you are insecure is a profoundly secure thing to do. Ironically, it takes a lot of confidence to admit you have character flaws.
Being secure is not about always being right or successful — far from it, it’s about being fine with the eventuality of having to look someone square in the eye and admit you were wrong, or ask for help when you have run into an obstacle you’ve found you cannot overcome alone.
It’s only the most insecure people who will attempt to hide their mistakes, or bludgeon their version of what’s true onto their surroundings when they risk being caught deficient.
Your typical schoolyard bullies are also very insecure by nature. While perhaps physically imposing, they use their reign of terror to avoid the risk of being called out on their deficiencies (be it social ability or smarts; whatever they’re insecure about).