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It might just be me but when someone in school asks to borrow a piece of paper. They're going to use the paper, so saying borrow would mean taking it and giving it back later. This is a minor pet peeve, so I'm not going to freak out if someone say it, but yeah...
Also I once asked my brother if I can borrow his water bottle and I immediately thought, "I don't think he'll want that water back..."