"The Rime of the Ancient Mariner" is a Romantic poem in that it offers up a picture of nature as an organic whole. Coleridge passionately believed that each and every creature in God's creation was joined together in a primal unity. From the highest to the lowest, all of God's creatures have their part to play in his creation. Even the humble albatross has his place in nature, which it is no one's business to disturb.
This would explain why the mariner brings so much misfortune on himself and his fellow shipmates by killing an albatross. In doing so, he has disturbed the intricate fabric of God's creation. As the mariner is part of the same organic whole as the bird, in killing it, he is killing a part of himself. If just one part of this whole should suffer, then we all suffer. In killing the bird, the mariner has unwittingly undermined the balance of primal forces that exists in the natural world, and he must suffer before that natural balance is restored.