The communication problems in "Home Burial" stem partly from the different ways that the characters address their grief. The man seems to have no problem carrying on with his everyday life, while the woman is totally inconsolable. Throughout the poem, you can see the ways that she gets offended by his lack of grief, and how he doesn't understand, and is frustrated by, her extreme sadness. In the end, they just can't understand each other, and they just can't get past the divide in their sadness.
People can handle grief in many different ways, so these two people should really cool it on each other.
This poem shows that one of the hardest parts about being sad is communicating about it, even with those closest to you.