Because all the evidence I've read or heard (most of it back in the 1980s) agreed on this. Specifically in a likely exchange between the U.S. and the USSR the northern, hemisphere would have been rendered completely uninhabitable within days. Humanity in the southern hemisphere would probably have lasted somewhat longer, but still would have been destroyed by nuclear winter and radiation. Details depend on the exact distribution of targets.

Remember Hiroshima and Nagasaki were 2 relatively small fission weapons. By the 1980s the USSR and the US each had enough much bigger fusion bombs to individually destroy the planet. The only question was how many each would use in an exchange and where they target them.