**Core Concept**
Progesterone is added to estrogen hormone replacement therapy (HRT) to counteract the proliferative effects of estrogen on the endometrium, thereby reducing the risk of endometrial hyperplasia and cancer. This concept is based on the understanding of the estrogen-progesterone balance in the menstrual cycle and its implications for endometrial health.

**Why the Correct Answer is Right**
The addition of progesterone to estrogen HRT is essential to mimic the natural menstrual cycle, where progesterone is secreted after ovulation. Progesterone helps to differentiate the endometrial cells, making them less sensitive to estrogen and reducing the risk of endometrial hyperplasia and cancer. This is achieved through the progesterone receptors in the endometrium, which are activated by progesterone, leading to the expression of genes involved in cell differentiation and apoptosis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not specify a condition that would necessitate the addition of progesterone to estrogen HRT. While some women may require progesterone, it is not a universal requirement.

**Option B:** This option is incorrect because it implies that progesterone is added to estrogen HRT only for women with a history of breast cancer. While progesterone may be contraindicated in women with a history of breast cancer, it is not the primary reason for adding progesterone to estrogen HRT.

**Option C:** This option is incorrect because it suggests that progesterone is added to estrogen HRT to increase the risk of endometrial cancer. This is the opposite of the actual effect of progesterone, which is to reduce the risk of endometrial cancer.

**Clinical Pearl / High-Yield Fact**
A mnemonic to remember the purpose of adding progesterone to estrogen HRT is "P-EACE": Progesterone to EASE (endometrial atrophy) and Counteract Estrogen's proliferative effects.

**Correct Answer: C. To prevent endometrial hyperplasia and cancer.**