I have a deep need to be right

May not apply to you, but one thing I've found useful is to occasionally make a point of intentionally saying or doing something you know is dumb while interacting with others. If you need to, maybe pretend you're Socrates, teaching others by asking them stupid questions you already know the answer to. Or maybe think of it as ironic comedy, like Andy Kaufman reading The Great Gatsby to his confused audience, primarily amusing himself. Whatever it takes to assuage your ego and let you actually put yourself out there doing something obviously dumb. Start however small you need to, and build from there.

It's not about your conscious, rational brain. You have to teach your underlying dumb, non-conscious, reflexive and emotional brain (which mostly runs the show) that the world won't fall apart if you do or say something "wrong." Instead, mistakes are like burning your toast at breakfast - not ideal, and now you're gonna be hungry until lunch and that's real and that sucks and you're angry about it, but in the grand scheme of your life a pretty small event.

Every big achiever in history has also made huge mistakes, and been at times massively inappropriate. Basically by definition - it's only a "risk" if failure is a real and looming possibility. If you want to make sure you're always right, you need to do the opposite and take as few risks as possible. And, to be clear, you will still fail. Because nobody is right all the time. That means with each passing day, your world gets smaller and smaller, because each new mistake is another direction that's off-limits.

Embrace failure. Otherwise, you're chasing a fiction, and ensuring that you won't have the tools to deal with it when the inevitable finally happens. And that's, by far, the riskiest choice of all.