**Core Concept**
The rejection of allografts, also known as transplant rejection, is a complex immune response that occurs when the immune system recognizes the transplanted organ or tissue as foreign. This process involves the activation of immune cells, such as T cells and macrophages, which target the allograft for destruction.

**Why the Correct Answer is Right**
The rejection of allografts primarily involves the activation of the immune system's cellular response, specifically the T cell-mediated response. T cells recognize the allograft as foreign through the recognition of major histocompatibility complex (MHC) molecules on the surface of the graft's cells. This recognition triggers a cascade of events that ultimately lead to the activation of T cells, which then orchestrate the immune response against the allograft. The activation of T cells is facilitated by the release of cytokines, such as interleukin-2 (IL-2), which promote the proliferation and activation of T cells.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because while the humoral immune response, involving antibodies and B cells, plays a role in transplant rejection, it is not the primary mechanism involved. The cellular immune response, particularly the T cell-mediated response, is the primary driver of transplant rejection.

**Option B:** This option is incorrect because while complement activation is involved in the immune response against allografts, it is not the primary mechanism by which rejection occurs. Complement activation is more of a secondary response, amplifying the immune response rather than initiating it.

**Option C:** This option is incorrect because while macrophages play a role in the immune response against allografts, they are not the primary cells involved in the rejection process. Macrophages are more involved in the secondary response, phagocytosing damaged cells and debris.

**Clinical Pearl / High-Yield Fact**
One key aspect of transplant rejection is the concept of immunosuppression, where medications are used to suppress the immune system's response to the allograft. Understanding the mechanisms of transplant rejection is crucial for developing effective immunosuppressive strategies to prevent rejection and ensure the long-term survival of the transplanted organ or tissue.

**Correct Answer:** C.