The black cockade was the color of the Hanoverian kings of England (think of the "King Georges"). When American colonists went to war in 1775, they still felt an affinity for their mother nation. After all, many of them were born there and still had relatives there. In fact, when George Washington's army was camped at Valley Forge during the winter of 1777-1778, the officers were still toasting King George. So it was natural that an American cockade would include the Hanoverian color black.
However, Americans also recognized the help that the French nation was giving them in gaining their independence from the mother country. And the color of French royalty was white.
Hence, the Americans adopted a black and white cockade for their emblem. In the painting, "Washington and His Generals at Yorktown" by James and Charles Willson Peale, you can see the black and white cockades on their hats.
This cockade became an emblem of the American War for Independence. In fact, it remained a patriotic statement for some time after the war as well. Not only was it incorporated on the United States Army's regulation shakos, but civilians also wore these patriotic devices. This one has a picture of George Washington in the center.
On July 4, 1798, the Philadelphia Centinel stated: "It has been repeatedly recommended, that our citizens wear in their hats on the day of Independence, the American Cockade, (which is a Rose, composed of black ribbon, with a white button, or fastening) and that the Ladies should add to the attraction of their dress...this symbol of their attachment to the government."
So over 60 years later, when the Civil War broke out, it was only natural for Southerners to revive the black and white cockade as the emblem for their Second War for Independence!
See my listing for a reproduction Black and White Secession Cockade here!