Which of the following is identified as a nail disease?

Onychia is the correct answer because it specifically refers to an inflammation of the nail matrix, which can lead to nail disease. This condition results in the swelling of the nail bed and can be associated with pus formation, discoloration, and in severe cases, the loss of the nail itself. Understanding nail diseases like onychia is crucial for cosmetologists, as proper identification and knowledge of treatment options are essential for maintaining the health and appearance of nails in clients.

In contrast, athlete's foot is a fungal infection primarily affecting the skin on the feet and does not involve the nails directly. Psoriasis is a chronic skin condition that often affects areas beyond nails, although it can cause nail changes, it is not classified primarily as a nail disease. Dermatitis refers to a general inflammation of the skin and can occur anywhere on the body; while it might affect the skin around the nails, it is not a nail-specific disease.