In the atheist's defense, you're attaching purpose and meaning to something that doesn't necessarily possess it in that little anecdote. A poem is a set thing, established in a set language. Something randomly happening and resulting in a specific result is unlikely. The analogy represented is flawed because it specifically reflects the views of a believer, and breaks down entirely once you remove that veneer and look at it objectively.
Look at it this way, you're aware of the other similar saying? The one about the watch? It goes, more or less, as follows:
Atheism can't be true because it's too far fetched. How could life evolve randomly? It's like taking all of the pieces of a watch, sticking them in a bag, shaking the bag up, and then pouring the contents out on a table and it resulting in a perfectly functional watch! It's just not possible to get that result from random stuff! It's too perfect, so the only answer is intelligent design!
There are a few problems with that, which ultimately make both ideas into terrible analogies.
First, they suggests the predestination of the human species and the world as it exists, which as a notion the atheist rejects. You're putting the pieces of a
watch in the bag and looking to get a
watch out of it. Or alternately you're taking a well of ink and getting a structured poem in an established language. It also suggests no waste, which means no evolutionary dead ends, no failed species rendered extinct, nothing beyond the desired result. This only makes sense if humanity and the world was
destined to exist, and it only ever existed in it's current, "desired" state. If this is the
correct result. Really, a more apt analogy would be to suggest putting any number or random parts into a bag, shaking it up, and having
anything of interest fall out when it was done, in addition to a bunch of random detritus that wasn't used in the end result. Or having a cat knock over an inkwell and have it result in a pretty splotch that could pass as abstract art.
Second, the other major problem with the idea is that it suggests that the world
works. Not just works, but works
well. You get a functional watch from the bag, and a beautiful poem from the cat? That suggests that the world is an awesome functional place. It suggests that ****
works. That's not true. Species go extinct. People malfunction and get cancer, or have aneurisms, or are still born, or any other number of defects. The world ravages itself with natural disasters and coldly ***** us with them. Sol is slowly breaking down and heading toward going nova. The entire world is barely functional, and often nonfunctional. It's barely contained entropy. We are all messy, imperfect things in a messy, imperfect world. So the proper analogy for the cat would instead be getting an ink spill that
looks vaguely like a few letters, but doesn't actually
spell anything out in any sort of coherent fashion, and with the watch that aforementioned random thing of interest that falls out of the bag? Well, all of those loosely connected parts would fall away from each other if you breathed on it heavily.
So yeah, bad analogy. I'm an agnostic. I don't think about whether there is or isn't a God much. I don't care much either way, as I'm quite happy sitting on my fence, but the analogy is deeply flawed regardless.