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Newspaper is made up of tiny wood fibers.
If you take a close look with a magnifying glass, you'll see that the fibers all line up in the same direction, up and down on the page. This gives the sheet of newspaper a grain. When you tear the newspaper from top to bottom it tears evenly because you are tearing in the direction of the grain. But when you tear it from side to side, it tears unevenly because you're tearing against the grain.