Great athletes don't think.
They are just great performers and for the most part they can't boil it down to what makes them so special. They might have a story they like to tell themselves but in reality it's a combination of things. When it comes to their confidence and lack of fear (that's what confidence is, not caring for the outcome and/or expecting a positive result) it all comes down to the thought processes in their head.
For starters, I would say you should focus on your strengths. When driving against your opponent it's a matter of what you focus on. If you EXPECT that he or she is going to reject you, and you actually believe that, you are very likely to get rejected because it's the self-fulfilling prophecy taking place.
What you expect to be true generally is. Instead, not only should you focus on the things that make you a better player (and the fact that you've come to this website) tells me that you are willing to improve. Some people play the game for the sake of playing the game. But not you, to you, basketball it's more than just a game.