why did ryuk kill light?

Because Light lost.

The whole Kira thing was nothing but amusement for Ryuk. Something that would ease his boredom. When Near (and to an extent - Mello) defeated Light, the "fun" was over.

Ryuk also brought up a rule regarding the Death Note stating that the Shinigami is obligated to kill the person who picked up the Death Note দ্বারা লেখা their name in the notebook when they die. He reminds Light about this rule as Light is practically begging for his life.

Ryuk specifically says the following;
"I told আপনি in the very beginning that I would be the one লেখা your name in the notebook when আপনি die. That is the rule between the Shinigami who brings the notebook into the human realm and the first human who picks up the notebook. If they put আপনি in prison, who knows when আপনি die? I don't want to just lie around waiting for আপনি to die, so it's all over. আপনি should die right here" (Chapter 107)

That's why he killed Light.