Step 1: Understand what the question is asking.
This is a NOT true question, so we need to find the one statement among the four that is false, while the other three are correct facts about varicocele.
Step 2: Recall the basic anatomy behind varicocele side preference.
A varicocele is dilation of the pampiniform venous plexus around the testis. The left testicular vein drains into the left renal vein at a right angle and is also longer than the right testicular vein, which drains more directly into the inferior vena cava at an oblique angle. The right angle drainage on the left raises venous pressure there, so the left side is affected far more often, roughly 80 to 90 percent of cases.
Step 3: Check each statement against this.
Option A says varicocele is more common on the right side. This is the opposite of the truth, since the left side is the common one, so option A is false.
Step 4: Confirm the other statements are true.
Option B, association with infertility, is correct, varicocele is a well known and treatable cause of male subfertility due to raised scrotal temperature and impaired sperm production. Option C is correct too, a new varicocele appearing on the left in an older man, especially one that does not empty on lying down, can be caused by a renal tumor blocking the left renal vein, so it should always prompt a look for a retroperitoneal or renal mass. Option D is also accepted teaching, that about 10 percent of varicocele cases are bilateral.
Step 5: Final answer.
Since options B, C, and D are true and only option A is false, the answer to this NOT true question is
\[ \boxed{\text{More common on the right side}} \]