Why did Ryuk wanted to kill light?

So, when Light was fatally wounded by the Near’s party, Ryuk decided that Light would no longer be entertaining, and decided to just kill him. This shows that he was never on Light’s side, just doing what he thinks would add to his entertainment (and supply of Apples).

Does Ryuk care about light?

As stated earlier, Ryuk is only following Light around for entertainment value. His little trip to Earth is basically a getaway from the boredom of the Shinigami world and a way to get a vacation from his Death God job for a while. This leads to the truth of the matter. Ryuk really doesn’t care about Light.