Why was Tom killed?

Silver killed Tom because he rebelled. When Tom found out that Silber was responsible for Alan's death... he walk away. In response, Silver shot a tree branch at Tom, breaking his back before stabbing him to death.

And with that, this brave fellow turned his back directly on the cook and set off
walking for the beach. But he was not destined to go far. With a cry John seized the
branch of a tree, whipped the crutch out of his armpit, and sent that uncouth
missile hurtling through the air. It struck poor Tom, point foremost, and with
stunning violence, right between the shoulders in the middle of his back. His hands
flew up, he gave a sort of gasp, and fell.

Whether he were injured much or little, none could ever tell. Like enough, to judge
from the sound, his back was broken on the spot. But he had no time given him to
recover. Silver, agile as a monkey even without leg or crutch, was on the top of him
next moment and had twice buried his knife up to the hilt in that defenceless body.
From my place of ambush, I could hear him pant aloud as he struck the blows.