Atoms need to be *really close* to each other in order to bond — on the order of the diameter of the atom itself (around one billionth of a foot). Jamming two sheets of paper together might *look* like they are “close” to our human eyes, but to atoms the two surfaces are actually barely even touching because the surfaces are extremely rough on the atomic scale, and there are other particles / air in between. (Also, atoms bond more easily with certain atoms than others — this is what chemistry is about!)
When two materials *are* bonded, they are bonded with a certain mechanical strength that is a property of the material, determined by the kinds of atoms and the structural arrangement they form. Cutting paper with scissors is one way of breaking the bonds between atoms in the paper. It works oin large part because the mechanical strength of the scissors is stronger than the paper — your hands push on the atoms in the scissors, which then translate that force into the paper.
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