Atomic size effect on critical cooling rate and glass formability in a model binary system is investigated using molecular dynamics simulation. To isolate atomic size effect from the rest of the factors that critically influence the glass formation, a hard sphere model is employed in conjunction with a newly developed densification method. The glass formability is defined as a set of optimal conditions that result in the slowest cooling rate of the glass-forming liquid. Critical cooling rates are identified from extensive molecular dynamics simulations. A kinetic glass-forming diagram is mapped out that marks the boundary between the glass-forming regions and competing crystalline phases in terms of the parameters of the atomic size ratio and alloy concentration. It is found that the potency of the atomic size difference on glass formation is influenced greatly by the competing metastable and equilibrium crystalline phases in the system, and the kinetic processes leading to the formation of these phases. The mechanisms of the atomic size effect on topological instability of crystal packing and glass formation are discussed.