To add to the other answers already here, on the atomic level, it’s electrons that are responsible for holding atoms ‘together’. This doesn’t make much sense in terms of our scale of reality, but the electrons “in” an atom, despite being very small, occupy a much larger volume than the nucleus. They can be ‘shared’ from one atom to another, and that’s how atoms stick together and form molecules. Individual atoms in the paper are stuck to adjacent atoms this way, but those big molecules are in turn just kind of mushed together and held together by a mess of fibres and adhesives all kind of tangled together – not the strong connections made by the sharing of elections. The metal in the scissors on the other hand is mostly held together by the sharing of electrons between all the iron atoms in a big ‘electron sea,’ a property specific to metals. This is basically what’s happening when scissors cuts paper: It’s very unlikely that anything in the paper would be strong enough to dislodge the iron atoms from each other, but the vastly weaker connections between “paper molecules” (really, the paper fibres) are very easy for the cutting edge of the scissors to get between and mechanically separate.
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