I had the same problem with this question and I know I'm late, but I am answering it for future students who may have trouble with this question. I believe the narrator is saying that if Helen Grey does not change her ways she will be unhappy. Men think she is beautiful, but because her personality is ugly they will find her unattractive. She will be bitter. In the poem it states, "Take heed, you yet may trip and fall, and no man care to stretch his arms."
In the poem "Helen Grey" by Christina Georgina Rossetti, Helen Grey is portrayed to be an unpleasant person. We know this because Rossetti states in her poem "But so you miss that modest charm / Which is the surest charm of all: / Take heed, you yet may trip and fall, / And no man care to stretch his arm." This implies that not many men care for Helen because her personality is unfriendly and unkind. This is implied again as Rossetti goes on to say "Stoop from your cold height, Helen Grey," Rossetti specifically chose to use the words "cold height." The word "cold" has the tendency to be used to add a harsh or an abrasive tone, often to a dark or unpleasant subject matter. The word height implies that Helen Grey is above everyone, which can be interpreted as mentally and not physically. Making this Rossetti's way of telling Helen Grey that she needs to get off of her high horse; in other words, Helen needs to face reality that being attractive does not make her better than the rest. Therefore, Helen Grey must be an unpleasant and narcissistic person.
The author's main purpose was the explain that the Community Service Council was effectual to high school students. The personal backstory was to add more evidence of the effectiveness.