White and Black are two poles labeled by the same category, Colour. But this is not the category what counter-position them as opposites. Within category colour, both this and that can reside inertly and alternate one to another from time to time without any tension implied by playing "opposite".
"Before" black could become an opposite to white, white itself must be attenuated as white in its core being. As @PeterJ put in his answer, "A contradiction must be A/not-A, and not A/B". So, white must first be able to emerge as not white. Negation of a being/identity of one pole is the necessary condition of the other (or some another) pole to start being its opposite.
Somebody here says, the opposite of A is not B but not-A. Not quite so. Not-A isn't being to have a status of something. Opposite is B, a something, however the prerequisite what makes it opposite to A is that A can not-be-A in its being A.
But the negation is not logical or linguistic trick, it is real. It is not a cognitive action (of mind playing with concepts like with cards); rather, it is what happens with a thing (such as this white paper) in the world. Our consciousness has pre-rational, intuitive apprehension of non-being aspect of things - because (to quote Sartre) consciousness or "human reality" is the only one thanks to which nonbeing comes to things.
Therefore it is silly to start with pure concepts and categories. Before that, there exists this white paper, which, as I look at it (while doing my current living process) inevitably corrupts into "not so white". The ulcer on the being (the deficit of white) gets paved by some imaginary compensation - and I begin to find the paper partly yellow. Yellow will be the opposite to white from now on. Then I skip my thoughts to the pen I was holding in preparation to write, I see the black scribble appearing - black is now the opposite to white. Pelican could be a perfect contrary to black (actually, I might find my paper devours ink like a white pelican).
So, white exists as meaningful attribute in my actions with the sheet and in incessant partial self-rejection which produces contraries without killing white.
Opposites are thus secondary, they pend on our intrinsic ability to attenuate identity of entities. Alternatives emerge in compensation to the lack of identity and in vague promise to restore it, the clearness of white paper, by a complement (black letters) via synthesis (paper with words written on it is potentially more white than it was before because it appears to excuse its whiteness by making it necessary for words to appear, not simply by colour contrast). Opposites nascend, initially, as near-by, not as poles far apart. The most opposite is a neighbour next door.