My first thought on seeing Vulkan is that it is basically Metal for everyone else. Is that not so? Then why would you expect Apple to support Vulkan given that they already have Metal?
Some history can also help. It all started from Mantle. Basically AMD grew tired of current APIs being behind the curve, and designed one from scratch that matches modern hardware approaches. Then Apple and MS used those ideas to push their lock-in off-shoots (they copied most of the ideas verbatim, working closely with AMD). Meanwhile, AMD simply opened up Mantle (they voiced this intention from the beginning) and gave it to Khronos as an initial proposal for Vulkan. The rest you probably know. So why exactly MS and Apple didn't get behind the shared effort? Because they are lock-in jerks. That's all there is to it.