You have to think about it the other way around: The constituents don't have binding energy. That energy becomes available when you let them bind, and you have to pay it back if you want to unbind them.
Example: If you have a proton and an electron, making a hydrogen atom will release about 13.6 eV (if it goes to the lowest energy state). You have to spend that 13.6eV to ionize the hydrogen, i.e. to get the electron far away from the proton again.
Example: If you have a proton and an electron, making a hydrogen atom will release about 13.6 eV (if it goes to the lowest energy state). You have to spend that 13.6eV to ionize the hydrogen, i.e. to get the electron far away from the proton again.