I always use oil on my stones, for a couple reasons.
1. The primary reason is that you need some kind of lubricant on Arkansas stones. If you don't use anything, the metal shavings get ground into the stone and it won't cut after a while. Lubricant doesn't completely prevent this, but it cuts down on it by a great deal. You can fix this by scrubbing or boiling the stones, but I'd rather avoid it in the first place.
2. Oil is fairly viscose; it stays on the stone without evaporating. Water works, but it's not ideal. Water is not a very viscose fluid, and it won't stay on the stone like oil will.
3. More subjectively, I like how it feels using oil vs dry or with water. It gives it a much smoother feel with better feedback imo