For me (and poems can have many interpretations), the poem is about the power of the non-rational over the rational.

And that ties in to the fate interpretation in this way: we think we’re in control of our lives, and that if we do the right thing (the rational thing), we can have a positive effect on our journey / outcome. This is a very rational way to approach life. It’s the mainstay of countless self-help books. But by definition, the rational mind has no control over the non-rational mind (whether it’s one own mind or someone else’s). The non-rational mind is always throwing a spanner into the works when you least expect it. The best you can do is accept the limits of your rationality, which doesn’t actually put you in control of your fate, but it means that at least you won’t be an accomplice in bringing about your own tragic outcome (like the dog in the poem or the thieves in The Ladykillers). And maybe you’ll get a chance just to abide.

Of course, in the Coen universe, the outcome isn’t always tragic. Sometimes it can be positive (Hudsucker Proxy) or mixed (Big Lebowski, Fargo) or indeterminate (Serious Man). If there were a single, predictable outcome, then the universe would be rational.