One of my friends is a kindergarten teacher, and a boy in her school was always trying to get the teachers to chase him. He loved being chased. Sometimes they'd do it, but his insistence on it got annoying. Eventually, the teachers collectively agreed to stop playing along. So what did the boy do? He started trying to chase the teachers, and the other students. Chasing and being chased are opposites. Opposites, though, are actually similar, because an opposition as a whole implies a small range of possibilities, all things considered. Other students like the slide.

Political campaigners know that you win by controlling the questions dominating public debate. The answers to the questions don't matter as much. An analytical linguist might claim that questions convey no information. But conversationally, asking a question is a polite way of suggesting something. And platitudes, which would sound ridiculous when negated, convey something too: the speaker chose them over other platitudes.

As another case, people are more defined by what they have opinions on than what those opinions are. Someone who thinks that the San Francisco black metal band Deafheaven plays badass melodious epics, and someone who thinks they play fake emo metal for posers, are way more similar than the 99% of us who've never heard of the band. When Jack Donaghy met his long-lost dad (30 Rock S3E21), they devolved within minutes into a heated debate about Tom DeLay. Jack: "Milton Greene and I are nothing alike!"