One of the first things that you will hear when you are learning how to climb is that you need to focus on your breathing. Grip strength, raw muscle and technique are all very important aspects of climbing, but if you do not have proper breathing when climbing, all of those skills do not matter. You could be a #1 ranked national bouldering champion, but if that champion stops breathing the way they have been trained to, their climb is going to significantly suffer.
The reason it’s so important, is that oxygen is a vital component and facilitator of most physical movements. When you grab onto a hold and tense all the muscles in your arm, your body sends signals letting your lungs know that they need to produce more oxygen. If your lungs are not providing the adequate oxygen intake that your muscles need, you fatigue. Your body starts to shut down because it can’t function without that valuable resource.
You get tired. You lose strength. You lose focus. Vital parts of your body start to slow down because you cannot fuel them with the oxygen they need.
There is no key trick to this. Breathing. Is. Easy. In through the nose, out through the mouth. And do not hold your breathe. Where we often fail is that we hold our breathe because we get so focused on what we are doing.