There were two main arguments for this policy of destruction which is exemplified by General William T. Sherman’s “March to the Sea.” Both of them have to do with the idea that this policy of destruction would be the quickest way to end the war.
One aspect of the argument has to do with tangible support for the war. The idea here was that the Union army could deprive the Confederate army of its ability to make war. If the US army went along destroying crops and railroads and other things, the South would no longer be able to supply its army. It would not have the supplies to give the army nor would it have any good way to get the supplies to the army. This would degrade the army’s ability to fight and would hasten the end of the war.
The second aspect has to do with morale. If the Union army were to embark on a policy of destruction, it would sap the morale of people in the South. It would make them feel that the war was lost and that they were being harmed by continuing to fight. This would make them more likely to demand that their government surrender.
In these ways, the policy of destruction was meant to cause the South to give up so the war could end more quickly.