With just a little work, and an educated guess or two, we can pretty easily work out some key information about the poem's speaker.
When we take into consideration the scholastic tone of the title and then consider who would ask "them" to carefully inspect a poem, the figure of a teacher is going to come up for most of us. Plus there's the fact that Collins himself is a teacher and is well known for his interest in promoting the art and appreciation of poetry in and out of the classroom. So, it seems like a slam-dunk: our speaker is a teacher.
But what about this teacher/speaker of ours? What is this guy really like? What makes him tick? What does he order at Starbucks? Mac or PC? Hybrid or muscle-car? Can we answer all these questions? No. But we can get a sense of this speaker's personality and state of mind from what he says and how he says it.
The speaker asks us to look at a poem in some very, well, weird ways. He isn't using words like analyze, explicate, or summarize. He isn't talking about symbols, images, or themes. He is talking about looking and listening and exploring. He describes the actions with a degree of wit and humor. He seems to care about what he is trying to say to "them," the students. In short, he sounds like a pretty cool dude—someone we wouldn't mind standing in front of us while we squirm in our uncomfortable desks. After all, he's trying to teach his students to appreciate art and not just complete an assignment.
But is our speaker satisfied with his results? The grim torture scene that takes place in the poem's final two stanzas would suggest otherwise. It appears that the speaker feels he is failing in his attempts to inspire his students to look at poetry in this unconventional way. The dark ending of this poem suggests that our speaker might feel a little disillusioned—try as he might, he can't get the students to stop torturing those poor, defenseless poems.
Frankly, it bums us out a little bit too. What'd poetry ever do to you?