Being confident doesn't necessarily mean being correct. It means you think you are correct.
If you are double checking your answers, that ensures you are correct and you can then be confident because you've double checked. But if you had to double check your answers, that means you weren't initially confident.
Acting confident in front of people reassures them of your expertise because it signals that you've done something enough that it's become ingrained in your memory or habits.
An example is a bus driver. I would want them to be confident about the route they are driving. If they are constantly checking a map at every intersection, I would be afraid they were not familiar with the area and might miss a turn if they misread the map even once.
Another example would be walking. Do you check your balance with every step you take? I'm sure you don't. And people around you don't actively watch you to make sure you don't fall. My infant, on the other hand, rebalances himself with every step and constantly holds onto steady things around him. Most people that watch him will be concerned about him falling because he's communicating a lack of confidence, a lack of experience.
You should definitely question your assumptions and approach things from a different angle. You will definitely end up with greater confidence. But if you do this in front of people you're displaying insecurity in your own assumptions and reasoning.