What motives did the two superpowers have for fighting surrogate wars

"Surrogate wars" also known as "proxy wars" are wars fought in a third country. The US and the Soviet Union were fighting each other in, for example, Afghanistan and Vietnam.

They preferred proxy wars, because they came without civilian victims of own population and without a distraction of the infrastructure of their own countries. In short, the two powers could compete militarily with each other without suffering the worst effects of the wars - this situation allowed them to try to defeat the other one without much risk to their own population.