No one is perfect. Likewise, no one is right all of the time.
That said, it's important to recognise the difference between having a competitive nature and the constant need to be right. When it comes to changing any bad habit, you can always start small. Use little opportunities to practice giving up the need to be right. It might be hard at first, but ultimately it can help you create a deeper, more fulfilled connection with your significant other.
Oftentimes the need to be right forces you to focus on the wrong. Instead of looking for what's wrong with what your significant other said or did, try to focus on what's right. By changing your focus, you shift your outlook and you'll notice there will be fewer opportunities to point out that they're wrong and you're right.