In general, you animate NURBS curves and NURBS surfaces by turning on the Auto Key button and transforming sub-object attributes such as CV or point positions, by animating the parameters that control dependent NURBS objects, and so on.
You can't animate NURBS object creation or creation parameters, or fundamental changes to NURBS geometry such as adding or deleting CVs or points, attaching objects, and so on.
Operations that Remove Animation
The following operations remove animation from a NURBS object or sub-object:
This operation removes the animation of anything directly dependent on the object.
Any operation that changes the number of points or CVs in a curve or surface removes the animation of all points or CVs that are lost.
The animation of the point or CV being fused to the other point or CV (the second one chosen) is lost. The first point or CV acquires the animation of the second.