Either/or or both??

I have noticed in recent years that people use the word "either" when it seems the word "both" would be correct. At times I don't understand what is meant by the speaker or writer when the word "either" is used. It sounds like there is a choice to be made when no such choice is available. Today, on the front page of the New York Times, I read the following: The attacks by the colonel’s troops on an oil refinery in central Libya and on cities on either side of the country unsettled rebel leaders — who have maintained that they are close to liberating the country — and showed that despite defections by the military, the government may still possess powerful assets, including fighter pilots willing to bomb Libyan cities. In reality, the colonel was attacking cities on both sides of the country but this article makes it sound like I, as the reader, have a choice as to the facts. Am I wrong? I hear this more and more often and recently tried to assemble something I had purchased but it wouldn't work because the instructions said "either" side when I later learned they meant "both" sides. I needed bolts on both sides to make it stable! I really think the word "both" is disappearing! I hear the word "either" used by news reporters and on television shows quite often. What gives? Did I learn this the wrong way . . . either/or ..... neither/nor....??