What leads to atopic eczema?

Atopy (see below) Asthma, eczema, & allergies are "atopic" diseases. "atopy" is an inherited tendency for developing any of these diseases. That being said... If you already have one of these diseases or have a close blood-relative who does, you have a higher risk (than those who don't) of getting any atopic disease. Note: an increased risk does not mean you actually will get any or all of these diseases.
Itching starts it. Atopic dermatitis or eczema is "an itch that rashes". Any problem that triggers itching can lead to this. Mild food allergies commonly cause itching in infants. But contact with dust mite particles on the skin, animal danders and even contact with staph or strep growing on the skin. Recently i helped a lady clear her severe atopic dermatitis by diagnosing her rare form of food allergy to meats.
Multiple triggers. The exact reason one gets atopic eczema is not clear, but likely a genetic tendency (atopic) and environmental influence. Environment could be allergic trigger (food, dust or pollen), or exposure to a substance that lead to skin itching then breakdown from scratching. Such irritant include dyes, sweat, fragrance, wool, heat, to name a few.