Many cancers are characterized by chromosomal instability (CIN). This phenotype involves the deletion and duplication of chromosomes or chromosome parts and results in a high degree of aneuploidy. The role of CIN for cancer progression is a very important, yet unresolved question. It has been argued that CIN contributes to cancer initiation because chromosome loss can unmask a mutated tumor suppressor (TSP) gene. At the same time, CIN is costly for the cell because it destroys the genome and therefore compromises clonal expansion. Here, we use mathematical models to determine whether CIN can accelerate the generation and expansion of TSP^-/- cells in the context of this tradeoff. Comparing cells with different degrees of CIN, we find that the emergence and growth of TSP^-/- cells is optimized if the rate of chromosome loss is of the order of 10^-3 to 10^-2. This result is very robust, is independent of parameter values, and coincides with experimental measures using colon cancer cell lines. However, if we consider all of the steps in the pathway, including the generation of the CIN phenotype from stable cells, then it turns out that the emergence and growth of TSP^-/- cells is never accelerated by CIN. Therefore, CIN does not arise because it accelerates the accumulation of adaptive mutations. Instead, it arises for other reasons, such as environmental factors, and is subsequently finetuned by selection to minimize the time to further cancer progression by means of the inactivation of TSP genes.