Neurons that fire together, wire together. There is a TED talk. Another name for it is neuroplasticity.
In the book, The Power of Habit, Charles Duhigg discusses this concept as the root of making positive changes in your life. It is hard to stop doing things, unless you do (choose to do) something different. Replacing an action with a new action is key.
Consider what you do when you fall. What is the first thing you do when the climbing gets hard? Look down? For a lot of people this would be the habitual action - look for where you will fall. Then you fall. The more times you repeat this - feel insecure, uncertain, look down, fall. This is repeated and becomes the habit that can prevent you from climbing harder.
Try this... just go to your local gym and watch people. Watch the same person climb a number of routes. Select a climber who is trying something that they will fall off or find very challenging and may fall. Notice if they look down OR if the fall trying.
Then notice your own choice.