**Core Concept**
Invasive lobular carcinoma (ILC) is a type of breast cancer that originates in the lobules of the breast, and it has a unique characteristic of spreading along the ducts and lobules, leading to bilateral involvement.

**Why the Correct Answer is Right**
ILC has a higher tendency to spread bilaterally compared to other types of breast cancer due to its diffuse growth pattern along the ductal and lobular structures. The cancer cells infiltrate the surrounding tissue and can easily spread to the opposite breast, making it more likely to be bilateral. This is in contrast to other types of breast cancer, such as invasive ductal carcinoma (IDC), which tends to present as a single mass in one breast.

**Why Each Wrong Option is Incorrect**
**Option A:** Invasive ductal carcinoma (IDC) is the most common type of breast cancer, but it typically presents as a single mass in one breast, rather than bilateral involvement.
**Option B:** Ductal carcinoma in situ (DCIS) is a non-invasive type of breast cancer that is confined to the ducts and does not typically spread to the opposite breast.
**Option C:** Phyllodes tumor is a rare type of breast tumor that can be benign, borderline, or malignant, but it is not typically associated with bilateral involvement.

**Clinical Pearl / High-Yield Fact**
ILC often presents as multiple small masses or a diffuse area of thickening in the breast, rather than a single large mass, making it more challenging to diagnose.

**Correct Answer:** C. Invasive lobular carcinoma.