The opposite of up is down.
The opposite of in is out.
Those two are easy. They are one-dimensional.
The opposite of Steve Jobs is Bill Gates.
Sort of. That's because Bill and Steve have a lot in common (outsize personalities, many Google matches, successful tech companies). But it's useful to consider them as opposites because we learn a lot about their approaches, personalities, and yes, brands, by looking at the inverse.
The opposite of Starbucks is Dunkin Donuts.
Not an independent coffee shop, and not coffee at home.
On the other hand, the opposite of Dunkin Donuts is not Starbucks. The opposite is 'not having coffee out.'
That's because when someone considers getting their morning coffee, the choice is usually home or Dunkin. That person doesn't have Starbucks as part of their choice set. Defining your brand in this way makes it easier to ignore the irrelevant competition and easier to figure out what you are (and aren't).
Bill Clinton and John Edwards aren't the opposite of Rush Limbaugh. Al Franken is.
The Blackberry isn't the opposite of the iPhone. A plain jane Motorola phone is. Apple understands this. Blackberry doesn't seem to.
The opposite of the Food Network is hours spent poring over cookbooks at a local independent bookstore. Or perhaps it's Good Housekeeping magazine. Or Gourmet...
One of the hardest things to do is invent a brand with no opposite. You don't have an anchor to play against.
Does your team agree on who your opposite is?