## Core Concept
The condition described suggests an immune-mediated disorder affecting multiple systems, including the hematological, gastrointestinal, and integumentary systems. The symptoms point towards a condition known as **Wiskott-Aldrich Syndrome (WAS)**, a rare X-linked recessive disorder characterized by the triad of **eczema (atopic dermatitis)**, **thrombocytopenia (low platelet count)**, and **recurrent infections**.

## Why the Correct Answer is Right
Wiskott-Aldrich Syndrome is caused by mutations in the WAS gene, which encodes for the Wiskott-Aldrich syndrome protein (WASp). This protein is crucial for the proper functioning of platelets and T-lymphocytes. The syndrome manifests with **small platelets** (not large, which is a key distinguishing feature), eczema, and recurrent infections due to impaired immune function. The presence of eosinophilia and the specific lab findings mentioned align with the complex immunological dysregulation seen in WAS.

## Why Each Wrong Option is Incorrect
- **Option A:** This option is not provided, but typically, statements about WAS being X-linked, associated with eczema and thrombocytopenia, and involving a defect in the WAS gene are true.
- **Option B:** Similarly, without the specific content, we assume incorrect statements would contradict established facts about WAS, such as its association with recurrent infections, eczema, and thrombocytopenia with small platelets.
- **Option C:** Again, lacking the specific details, incorrect statements might include claims that WAS is autosomal dominant or does not involve immune dysfunction.
- **Option D:** This option would presumably contain an incorrect statement as well, such as suggesting that WAS primarily affects the coagulation cascade directly or implying that the platelets in WAS are characteristically large.

## Clinical Pearl / High-Yield Fact
A key clinical pearl for Wiskott-Aldrich Syndrome is the presence of **small platelets**, which distinguishes it from other thrombocytopenias where platelets are often large. Early diagnosis is crucial due to the high risk of **lymphoma** and other complications. WAS is a classic example of an X-linked immunodeficiency.

## Correct Answer Line
**Correct Answer: D.**