Most white flowers are not pure white; they have subtle shades of yellow, pink, green, or blue. As you do, you'll discover what combinations work for you. You will have to play with the plants and hold them next to each other, to really appreciate the differences.
There is no one way to create a white garden and more often than not, White can have a cooling effect when paired with other colors, but an all-white garden can easily become a glaring blur. the addition of a secondary shade gives the garden dimension and makes the white more prominent.