Besides looking at the subject matter of poems, describe what additional subject matter you would suggest as possible writing topics for poems?

It sounds like you are wondering how to write about or
"analyze" poetry.  Depending on the specifics of your assignment, I can provide a couple
of ideas.

First, you can look at the purpose or meaning of
the poem.  This means thinking about both the author and
the intended audience, as well as the technical elements of the poem.  Technical
elements includes things beyond the subject (or theme) of the poem, like images,
figurative language, the speaker (or voice), or symbolism.  You can also analyze
structure and sound elements.  As you analyze any of these elements, you can tie them
back to the main subject of the poem to help you determine their
meaning (or the author's
purpose).

Second, you can react personally to the poem. 
Talk about what appealed to you and why.  Whether you experience an emotional reaction
or not, it is always appropriate to relate ideas/details in the text to personal
experiences, observations, or other things you've read.  This is why literature is such
an organic and sustainable subject.  Though the texts may not change, the reader does,
and discussion of reaction and application is why we continue to explore the written
arts.

The most important thing I tell my students when
reading poetry, is not to "shut down" and simply say, "I don't get it."  Pick one thing
you think you understand and build from that.