What were the reasons for Sherman's march through Georgia and Carolina?

To end the war quicker, by attacking the civilian infrastructure that supported the Confederate armies in the field, and starve them into surrender.

In ay case, the other option was proving impractical. Grant had ordered him to destroy the Army of Tennessee. He had failed to do this, and meanwhile his supply line was dangerously long and vulnerable. Turning in the other direction, and crossing Georgia, he could live off the land.