Advanced tumor growth requires the formation of new blood vessels (angiogenesis). Whether new blood vessels are formed or not depends on a balance between angiogenesis inhibitors and promoters. Host tissue, as well as tumor cells, express inhibitory factors preventing angiogenesis. During cancer progression, tumor cell lines evolve which produce factors promoting the angiogenic switch. We use mathematical models in order to examine the conditions required for angiogenic cell lines to emerge and hence for the disease to progress. We find that genetic instability, defined as a much elevated mutation rate of somatic cells, is required for the emergence of angiogenic tumor cells. This is because a high mutation rate ensures that within a short period of time, a sufficiently high number of angiogenic cells are generated. This founder population of mutant cells is large enough to overcome the inhibitory factors produced by the tissue thereby inducing the angiogenic switch through the production of promoters. In the absence of genetic instability, angiogenic cells cannot fix, even if the relevant mutations are generated at low levels in the tumor cell population. This is because angiogenic promoters will not be sufficiently abundant to counter the influence of inhibitory factors. In this context, the inhibition of angiogenesis can be viewed as a host defense ensuring that the tumor need be genetically unstable if it is to grow and progress beyond a certain size limit. We observe that genetic instability is of value early in tumorigenesis but becomes a liability later. This is because instability decreases the fitness of the angiogenic tumor once it has become established.