Why free neutrons are usually produced in a Nuclear Fission? The production of neutrons is a feature of fission reaction. Usually 2-3 free neutrons are produced in the fission. Why is that so?
 A: Heavy nuclei have more neutrons per proton, so when they split into lighter nuclei, neutrons are left over.
Here is a version of the Karlsruhe Nuclide Chart:

Plotted from bottom up are the chemical elements in increasing proton count, i.e. hydrogen is a bottom row, calcium and lead are indicated to come further up. Plotted to the right are increasing neutron numbers, i.e. the various isotopes of the elements. With the example of the bottom hydrogen row, there's first hydrogen on the left, then deuterium, and tritium to the right.
Stable isotopes are shown in black. Everything colored is radioactive. Blue isotopes beta decay, red ones decay via electron capture, yellow isotopes decay by emitting an alpha particle.
Now, I also drew a green line at a 45 degree angle. This is the line where isotopes have equal number of protons and neutrons. As you can see, as elements become more and more heavy (have more protons), they need even more neutrons to remain stable (the chart of nuclides bends to the right). This is because protons are positively charged and thus repel each other; Neutrons provide the nucleus with sufficient Strong force to over-compensate for that repulsion, rendering the nucleus stable.
When you now break up one of these heavy, neutron-rich nuclei, you may of course end up with isotopes that have exactly half the number of protons or neutrons, but these would not usually be stable due to an over-abundance of neutrons. Typically you would end up with isotopes marked blue, which beta decay, thus converting a neutron in a proton plus an electron. For heavy nuclei like uranium and such, some neutrons (2-3 as you correctly indicate) even get ejected right away as free neutrons.
(And for the smarty-pants, yes, I know, the Karlsruhe Nuclide Chart has the neutron as the bottom row ;) )
