Our bodies are extremely efficient at using carbohydrates and even fat for fuel, but in a typical moderate intensity workout, protein contributes very little. In endurance and/or resistance training however, once carbohydrate fuel stores run out, significant protein catabolism takes place, depleting those stores as well.
It is important to understand that our muscles do not store protein. Amino acids can be found in 3 places: bound muscle protein, muscle intracellular free amino acid pool, and then the free amino acid pool in the blood. These molecules are constantly moving and changing to perform both protein breakdown and synthesis. During recovery, BOTH protein breakdown and protein synthesis increase. By consuming a high-quality/complete protein snack (a protein with all the essential amino acids, typically an animal source or combining two incomplete proteins) within an hour of exercising then helps to even out synthesis and breakdown. This is significant for athletes because when we break down more amino acids than we take in, our muscles begin to shrink.
Keep in mind that we also need an energy source to help our bodies repair. Pairing a high-quality protein with a carbohydrate prevents protein from being metabolized for energy so that it can do its job in synthesis and breakdown.