The whole poem is an extended paradox.
The Extended Paradox of Dead Man Speaking
Readers of A.E. Housman's "Is My Team Ploughing" will likely react to the impossibility of a dead man holding a conversation with a living man. That reaction will depend on how literally one takes the conversation. Obviously, a literal conversation is impossible; thus, one must consider the fact that the conversation itself is a figure of speech, an extended paradox. Paradoxes, which at first seem absurd, are justified upon further explanation. But how does one justify a conversation between a dead man and a living man? Only the living man can be offering a report of this conversation; thus, the dead man’s part of the conversation is also coming from the mind of the living man.
But why would a living man hold such a conversation, even if imaginary? The answer is that the living man is being tormented with guilt at the way he treated the dead man while the latter was living, and now that his so-called friend is dead, he is committing the ultimate sin against their friendship by taking his place with the dead man’s sweetheart. The living friend is merely attempting to assuage his own guilty conscience by holding the imaginary conversation in which he attempts to solace his former friend.