Destroy not destroying GameObject

I have the following code in Unity3D for adding and deleting a line segment for a 3D drawing:

public class LinearPiecewiseTrajectory : MonoBehaviuor
{
    private List<LineSegment> lineSegmentRep;

    //other stuff here

    public void addSegment()
    {
        GameObject lineSegmentObject = new GameObject();
        lineSegmentObject.name = "LineSegment";

        LineSegment lineSegment = lineSegmentObject.AddComponent<LineSegment>();

        lineSegmentObject.transform.parent = this.transform;
        lineSegmentRep.Add(lineSegment);
    }
}

public void deleteSegment(int i)
{
    Destroy(lineSegmentRep[i]);
}

LineSegment is a MonoBehavior I have defined.

However, this destroy call isn't actually destroying the LineSegment object. The only discernible behavior I can find is that it's setting the old LineSegment's geometric transform back to identity.

What am I missing?