**Core Concept**
The question is testing the understanding of the relationship between specific immunoglobulin subclasses and their role in protecting against infections caused by encapsulated bacteria. The child's recurrent sinopulmonary infections suggest a defect in the immune system's ability to fight these pathogens.

**Why the Correct Answer is Right**
The correct answer is related to the function of IgG2 in protecting against encapsulated bacteria. IgG2 is the primary antibody subclass responsible for providing immunity against polysaccharide-rich capsules of bacteria such as Streptococcus pneumoniae, Haemophilus influenzae, and Neisseria meningitidis. This is because IgG2 antibodies are more effective at recognizing and binding to the polysaccharide components of these bacterial capsules.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because IgG1 is the most abundant subclass of IgG and is primarily involved in protecting against protein-rich antigens, not polysaccharide-rich capsules.
**Option B:** This option is incorrect because IgG4 is the least abundant subclass of IgG and is not primarily involved in protecting against encapsulated bacteria.
**Option C:** This option is incorrect because IgA is a different class of immunoglobulin that plays a crucial role in mucosal immunity, but it is not specifically related to the protection against encapsulated bacteria.

**Clinical Pearl / High-Yield Fact**
A deficiency in IgG2 can lead to an increased susceptibility to infections caused by encapsulated bacteria, particularly in children. This is often referred to as "IgG2 deficiency" or "IgG subclass deficiency."

**Correct Answer: C. IgG2**