Is it more important to breathe or to eat?
The answer to your question is that it is far more important to breathe than to eat as your body can survive for days without food but must have air all the time. A body without air can die, suffer brain damage, or be put on a machine to provide the necessary oxygen. Think about the length of time you can hold your breath. During that time, your brain is deprived of oxygen, and you simply must give in and breathe. Now think of eating. Though we love to eat good food, food itself is not the necessity that oxygen is. Fasting for a day or more really doesn't deprive the body, but being without oxygen is life-threatening.