In Billy Collins' poem, "Introduction to Poetry," what does the poet means by "torturing" a poem to get its meaning?

To put this quote into context, take a look at the previous lines of the poem. In essence, the speaker argues that students of poetry do not really dig into a poem to discover its true meaning. They do not analyse the poem by looking at it critically (like holding up a “color slide”), for example, nor do they listen to the sounds of the poem, like putting one’s ear against a “hive.”

In contrast,...

To put this quote into context, take a look at the previous lines of the poem. In essence, the speaker argues that students of poetry do not really dig into a poem to discover its true meaning. They do not analyse the poem by looking at it critically (like holding up a “color slide”), for example, nor do they listen to the sounds of the poem, like putting one’s ear against a “hive.”

In contrast, the speaker says that students torture a poem in the hope of revealing a “confession.” This is an example of a metaphor in which the speaker compares his students to torturers who use brute force and violence to make their victim speak. In this case, the victim is the poem itself (which is also an example of personification). Specifically, the poem is a victim of the students’ oppressive tactics, forced to make its true meaning obvious to the reader without being allowed to keep any of its secrets. 

By characterizing students in this manner, the speaker portrays them as aggressive and bullying. In other words, he criticizes their lack of genuine interest in understanding the meaning of a poem and highlights their inability to be analytical. Arguably, the speaker wants his students to be the very opposite of this: he wants them to view the study of poetry as a creative challenge and to accept this challenge wholeheartedly.