A speaker shuts the door on a dog on a cold, wet day. The dog isn't being a nuisance. The poem says it "did not intend to trouble me," and that small detail makes the moment feel a little guilty. The trouble is not what the dog does but what it stands for: "the shortness of time / and muchness of fur." A dog's brief life and its warm, shaggy physical presence seem to bring up feelings the speaker would rather avoid, perhaps about loss, or about how quickly life passes.
So the speaker turns away, almost pleading: "o leave me to my life / in the factory of maybe." That last image is striking. It suggests a life of endless possibilities and indecision, busy and mechanical, but not exactly warm. The mood is wistful and quietly rueful. The speaker seems to know that closing the door is a retreat, and the poem leaves us sitting with that discomfort.