A refined logic:
Let T is stopping time. Then {T=n} is Xn measurable, {T=n-1} is X(n-1) measurable and hence Xn measurable and continuing in this way... {T=1} is Xn measurable.
Therefore {T=n}U{T=n-1}U...U{T=1}={T<=n} is Xn measurable. so, {T>=n+1} is Xn measurable which is a contradiction.