Answer:
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.
Explanation:
We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.