In order to remove a neutron you have to fire a projectile into the nucleus to dislodge the neutron. The thing is, you can't be sure of the structure of the nucleus and where exactly the protons are and where exactly the neutrons are. As a result, you can't guarantee that you will eject a neutron if you fire a particle or beam of energy at the nucleus. Imagine the nucleus as a hodge-podge of two different colored spherical magnets. The protons are red and the neutrons are blue. They are both the same size. Now you take a whole bucket of the magnets and blindfolded you reach your hand into the bucket and grab a handfull. After taking your handful of red and blue magnets you count the number of red spheres (protons) and the number of blue spheres (neutrons) that are affixed to each other. (You basically calculate the mass of the isotope you have). Now take this mass of protons and neutrons and suspend it in a stream of upward moving air so that it kind of "floats" on top of this stream of air. Get in a car and drive about a football field's length away. Now take out a gun that fires small little bee-bees at the spinning "nucleus" at the other end of the field and accurately knock off only ONE neutron. See the problem?
The nucleus is so small and the particles arranged in such a random manner that you can't accurately predict what you'll be knocking off. In addition, because of the attraction between the particles, you have to use either a large projectile, or a projectile with a lot of energy. The projectile with a lot of energy will undoubtably break the nucleus apart into many fragments (fission), or will be so massive that it won't knock off just one particle. If you don't fire it with enough energy, it will just bounce off the nucleus or become absorbed by the nucleus.