The sentence is not a fragment. It’s inane and stylistically inept, but it’s syntactically complete.

The matrix of the main clause follows a subject-linking verb-complement structure: “this quote is a reminder …”

The complement contains a content clause. The subject of the content clause is a gerund phrase: “standing by each other”, and the verb in this clause is finite, as it should be.

There are multiple issues with this sentence, in style and substance, that go far beyond anything a simple fix could do even it were a fragment.

A side note: I’m curious if the teacher marked the sentence this way because of “for”. I’ve run across teachers in the past who mark sentences beginning with the FANBOYS words as incorrect because they believe that such creates a fragment. 

On Oct 5, 2014, at 6:55 AM, Geoffrey Layton <[log in to unmask]> wrote:

> I'm a member of a listserve populated by AP English teachers (primarily lit but also comp), and the following issue has recently arisen. Please comment - I would very much appreciate it (I won't tell you how I commented just yet - I'd like to get your views): 
> 
> Please read the following and tell me if you would consider the last sentence a fragment:
> 
> "This quote from Beowulf exemplifies not only the best of man but he worst of man as well. For this quote is a reminder to all that  standing by each other, through thick and thin,is the real test of being a man of true worth." 
> 
> The paper from which this is taken is extremely weak in content, wording, and mechanics.This is marked as a fragment and with two fatal errors (she has another which the parent admits is a fragment), the rubric being used gives the student a score of 50 and, of course, the parent is questing (sic) this one sentence and is thinking it if it is changed to non-fragment her daughter will receive a B on the paper--but that is another argument.
> Please respond ASAP. The principal, the teacher who scored the essay, the parent, and I  have a meeting Monday. Exams are Wednesday and Momma wants a B.
> 
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