**Core Concept**
The clinical presentation of itchy skin lesions with extensor distribution on the skin, particularly on the elbows, combined with a history of bronchial asthma, suggests an allergic condition. This scenario is characteristic of atopic dermatitis (eczema), a chronic inflammatory skin disease often associated with allergies and asthma.

**Why the Correct Answer is Right**
The child's symptoms are suggestive of atopic dermatitis due to the involvement of extensor surfaces, which is typical in children, and the presence of asthma in the family history. Atopic dermatitis is a complex condition involving an interplay between genetic predisposition, environmental factors, and an impaired skin barrier. The disease is characterized by chronic inflammation, immune dysregulation, and the release of various cytokines and chemokines, including IL-4, IL-5, and IL-13, which contribute to the development of skin lesions and asthma.

**Why Each Wrong Option is Incorrect**
**Option A:** The presence of itchy skin lesions and asthma in the family history does not suggest psoriasis, as this condition typically presents with well-defined, scaly plaques, not itchy lesions.

**Option B:** Contact dermatitis is a type of skin reaction to external allergens or irritants and does not typically present with a family history of asthma.

**Option C:** Seborrheic dermatitis is a condition characterized by scaly, oily patches on the skin, particularly on the face and scalp, which does not match the child's symptoms.

**Clinical Pearl / High-Yield Fact**
Atopic dermatitis is a chronic condition that requires long-term management, including topical corticosteroids, moisturizers, and phototherapy in severe cases. Early recognition and treatment can improve quality of life and prevent complications.

**Correct Answer:** A. Atopic dermatitis.