As espoused in From Chance to Choice, liberal eugenics is a system which seeks to apply John Rawls’ Theory of Justice to the field of genetics. In Rawls’ system, to simplify it a bit, the fairest system is one in which shares are distributed as evenly as possible. If you imagine you are tasked with dividing a cake, but you don’t know which slice you will get in advance, rationally you will divide it as evenly as you can. The same logic applies to social shares - from a rational perspective you would find it unfair if shared were distributed too unequally.
The Rawls school apply this principle to genetics and claim that, in order to promote a level playing field, we ought to use the powers of genetic technologies to remedy the so-called genetic “deficiencies” that put some people at an unfair disadvantage compared with others.