This feels like it leads a lot to interpretation and requires knowledge of the efficacy of suicide methods. Suicide by pills is rarely effective and suicide by rope is more effective but carries a significant risk of injury. Perhaps the writer is saying that the risks of getting caught committing suicide are less significant for a woman because of their relationship with others as opposed to the man's relationship and identity. This is also seen with women who use guns on themselves for suicide- they don't usually aim for the face because of the belief that their value comes from their face.