When you extract an object, Photoshop erases its background to transparency. Pixels on the edge of the object lose the color components derived from the background, so they can blend with a new background without producing a color halo.
For superior results and nondestructive processing, use the Select > Refine Edge command. See Refine selection edges for instructions and links to additional helpful tutorials.
The Refine Edge command is particularly impressive with highly complex edge content such as wispy hair. Unlike the older Extract plug-in, which permanently erases pixel data, the Refine Edge command creates selection masks that you can later readjust and fine-tune.