lack of distance cues. The rainbow you see is actually a three-dimensional cone with the tip at your eye.
Consider a glass cone, the shape of those paper cones you sometimes see at drinking fountains. If you held the tip of such a glass cone against your eye, you would see the glass as a circle. All the drops that disperse the rainbow's light toward you lie in the shape of a cone of different layers with drops that deflect red to your eye on the outside, orange beneath the red, yellow beneath the orange, and so on all the way to violet on the inner conical surface. The thicker the region containing the water drops, the thicker conical edge that you look through.
Your cone of vision that intersects the cloud of drops that creates your rainbow is different from that of a person next to you. Everybody sees his or her own personal rainbow.
If the Earth were not in the way, a rainbow would be a complete circle. This is why you will never find the golden pot at the end of the rainbow.