Which of the following is a flying insect that feeds on skin, nasal, and eye secretions but does not bite?

Face flies are indeed the correct answer because they are known for their feeding behavior on the secretions of the skin, eyes, and nose of livestock, particularly cattle. Unlike other flies that may have more aggressive biting or feeding habits, face flies do not bite animals. Instead, they utilize their long mouthparts to lap up fluids, especially those surrounding the eyes and nose. This feeding style is particularly relevant in understanding the impact of face flies on livestock health, given their role in transmitting diseases, rather than simply inflicting pain through bites.

In contrast, Tabanid flies, commonly known as horse flies, are notorious for their biting behavior, which can cause distress and injury to animals. Fruit flies are primarily known for their role in decomposing organic matter and typically do not feed on animal secretions. Horse flies also fall into the biting category, so they are not suitable answers since their behavior disturbs livestock significantly through painful bites. Thus, face flies are uniquely characterized by their non-biting feeding habits, which is why they are the correct choice in this situation.