**Core Concept**
The child's eczematous dermatitis on extensor surfaces, combined with the mother's history of bronchial asthma, suggests an underlying allergic predisposition. This scenario is consistent with a condition that involves atopic dermatitis, asthma, and allergies, collectively known as the Atopic March.

**Why the Correct Answer is Right**
The Atopic March is a term used to describe the progression from atopic dermatitis in early childhood to asthma and allergies in later childhood. The child's eczematous dermatitis on extensor surfaces is a common presentation of atopic dermatitis. The mother's history of bronchial asthma further supports the diagnosis of the Atopic March. This condition is often associated with an imbalance in the immune system, leading to an overactive allergic response. The underlying mechanisms involve an increased expression of Th2 cytokines, which promote the production of IgE antibodies and the activation of mast cells.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect as it does not relate to the Atopic March or the child's presentation of eczematous dermatitis.
**Option B:** This option is incorrect as it is unrelated to the child's condition and the mother's history of asthma.
**Option C:** This option is incorrect as it does not accurately describe the Atopic March or the underlying mechanisms involved.

**Clinical Pearl / High-Yield Fact**
The Atopic March is a significant clinical entity that highlights the importance of early recognition and management of atopic dermatitis to prevent the development of asthma and allergies.

**Correct Answer:** D.