A village was planning a feast. All of the residents were asked to bring a bottle of wine, each of which would be mixed together in a large vat for everyone to partake of. One of the residents reasoned that a single bottle wouldn't make a difference, and so brought a bottle of water instead. When it came time to distribute from the vat of wine at the feast, it turned out the vat was entirely full of water, as all of the residents had come to the same conclusion.
For nearly every practical purpose in our United States general elections, a single vote does indeed not make a difference. But a thousand votes might make a difference, and if those thousand people were all persuaded that their single vote wouldn't make a difference, and then didn't vote, then the difference would not be made.