**Core Concept:** Priapism is a condition characterized by prolonged and persistent erection, often due to various causes. Increased desire to pass urine is a symptom of bladder dysfunction or overactive bladder (OAB). Both priapism and OAB are clinical manifestations of a common underlying cause.

**Why the Correct Answer is Right:** The correct answer (Option C) is methotrexate, a cytotoxic drug used in cancer treatment and autoimmune disorders. Methotrexate can cause priapism due to its effect on the central nervous system and inhibition of phosphoribosyl pyrophosphate synthetase, leading to impaired cellular proliferation and repair. Additionally, methotrexate can cause OAB by damaging the bladder smooth muscle and nerves, leading to increased bladder contractions and detrusor overactivity.

**Why Each Wrong Option is Incorrect:**

A. Cyclophosphamide (Option A) is a similar cytotoxic drug that does not cause priapism but may cause other side effects like hemorrhagic cystitis, which can lead to OAB.
B. Glucocorticoids (Option B) are anti-inflammatory drugs and do not cause priapism or OAB due to their indirect effect on the central nervous system and smooth muscle cells.
C. Methotrexate (Option C) as explained above is the correct answer.
D. Nitrates (Option D) are used in angina treatment and do not cause priapism or OAB.

**Clinical Pearl:** Understanding the mechanisms of these medications helps in recognizing and managing the side effects they cause, ensuring appropriate patient care and treatment decisions.