What explanation does the demon's prisoner give the brothers for why she collects her lovers' rings?

The rings that she collects from her lovers is a simple proof to show that women can do whatever they want and attain whatever they desire.

Explanation:

In "The Arabian Nights", the two brothers had just experienced that their respective wives had cheated on them. Shahrayar's wife had slept with the cook while Shahzaman's wife had slept with a slave. So, they both secretly went to the desert to look for a man whose life is more wretched than theirs.

But their encounter with the genie / demon shows that their lives are not that wretched as they thought. The genie had a beautiful as a wife, but enclosed in a glass box. Whenever he sleeps, she comes out and sleep with other men, 96 in all. She also sleeps with the two men making the count to 98 for she keeps the rings of her victims / conquests. She declares "to think that jealousy and restraint can preserve a mistress, notwithstanding thy vigilance." This decision to collect the rings of the men (most probably as trophies) is proof to show that women can do whatever they want and are capable of achieving whatever they desire.