prove that a closed walk of odd length contains a cycle.

i am able to proceed upto this stage:

a closed walk may be like this v1,v2,........,v1

now,if all the points are distinct in the walk,then the given walk represents a cycle.

& if suppose a point,say v, is the first point in the walk to be repeated,then if we start from the first v to the repeated v then it will form a cycle.

but i am not able to understand why a closed walk of odd length is required.