Learn Turkish: Seni rencide etti diye o insafsız adamı hiç savunur muyum? - Would I ever defend that cruel man because he offended you?

This is a rhetorical strong negation using the aorist tense. By combining hiç (ever/never) with the aorist question savunur muyum (would I defend), the speaker isn't actually looking for an answer. They are emphatically stating, "I would absolutely never defend him!"

How does diye work in this sentence?

You probably first learned diye for quoting someone. However, here it means "because" or "on the grounds that". The clause right before it, Seni rencide etti (He offended you), acts as the reason for the rest of the sentence.

Why use the aorist savunur muyum instead of the present continuous savunuyor muyum?

The aorist is often used to talk about general willingness, habits, or hypothetical actions. Using savunuyor muyum would mean literally "Am I defending him right now?", whereas savunur muyum translates more to "Would I ever defend him?" This fits the rhetorical nature of the sentence perfectly.

What exactly does rencide etmek mean compared to other words for hurting someone?

Rencide etmek is a slightly more formal or strong way to say "to offend", "to hurt someone's feelings", or "to humiliate". It implies causing emotional pain or damage to someone's pride, which explains the speaker's strong reaction in this sentence.