Throughout history poets have struggled with the rules of society. Many different literary movements came about as a reaction to the period which an author found them self in at the time.
As for how poetry makes one human, one can look at multiple different poetic genres to examine what it means to be human. While not in a poem, the most prominent quote that comes to mind is in Richard Connell's short story "The Most Dangerous Game."
"But no animal can reason," objected Rainsford.
"My dear fellow," said the general, "there is one that can."
To fully understand what makes someone human is through the definition of the word itself. The best "poetic" definition comes from Merriam-Webster:
susceptible to or representative of the sympathies and frailties of human nature.
Therefore, any poem which examines a human's ability to reason or the frailties of human nature would speak to the fact that "poetry explores what it means to be human."
Frailties speak to the weaknesses which only mankind can exhibit: sadness, love, fear, worry (to simply name a few). While some would argue that some animals exhibit some characteristics typical of humans, they assuredly do not have the capability to possess them all. Only humans can.
Therefore, any poem which examines the sympathies and frailties of mankind would explore humanity.
One example is "A Red, Red Rose" by Robert Burns. While animals MAY be able to show love (or what a human determines as love) they cannot express it in the same way as humans. No animal is capable of expressing love in the same way Burns does--or other poets depicting love.
Another example of a poem which speaks to being human is "Sadness and Joy" by William Henry Davies. In this poem, Davies speaks to both sadness and joy as if they were human. Humans are the only beings which can give characteristics such as the ones depicted in the poem (personification) to inanimate objects. We, as humans, speak of love, pain, all emotions as if they could walk and talk and speak. No animal has the ability to do that.