If you find a bug in your copy-paste code, you will need to fix it every place you did and hope you can remember them all (this also holds for changed requirements).
If you keep logic in one place, it is easier to change when needed (so if you decide that the application needs updating, you only do it in one place).
Have your boss read about the DRY principle (Don't Repeat Yourself).
What you are describing sounds like the perfect use for libraries, where you share code and only keep it in one place.
I would only ever copy-paste code if I intended to refactor it soon after - making sure I later on extracted common code so I could reuse as much logic as possible. And by soon after, I mean minutes and hours later, not days and weeks.
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