Carl Sagan's ideas on the self-extermination of technological civilizations
It sounds like what you may be referring to is Fermi Paradox:

The Fermi paradox — or Fermi's paradox — is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations, such as in the Drake equation, and the lack of evidence for such civilizations. The basic points of the argument, made by physicists Enrico Fermi (1901–1954) and Michael H. Hart (born 1932), are:

The Sun is a typical star, and there are billions of stars in the galaxy that are billions of years older
With high probability, some of these stars will have Earth-like planets, and if the earth is typical, some might develop intelligent life.
Some of these civilizations might develop interstellar travel, a step the Earth is investigating now.
Even at the slow pace of currently envisioned interstellar travel, the Milky Way galaxy could be completely traversed in about a million years.


-Wikipedia: The Fermi Paradox
In 1966, the book Intelligent Life in the Universe originally written by I.S. Shklovskii and extended by Carl Sagan &quot;speculated that technological civilizations will either tend to destroy themselves within a century of developing interstellar communicative capability or master their self-destructive tendencies and survive for billion-year timescales.&quot;(4)
This review of the book written by E. J. Öpik, questions what, if any, factual information was presented.
In 1983, Sagan cowrote an article for the Quarterly Journal of the Royal Astronomical Society with William I. Newman entitled The Solipsist Approach to Extraterrestrial Intelligence that also addresses the issues of the self-extermination of technological civilizations.