Carl Sagan's phrase "The absence of evidence is not the evidence of absence" is a criticism of the argument from ignorance found in "The Fine Art of Baloney Detection".
Carl Sagan compares the phrase "the absence of evidence is not evidence of absence" to an "appeal to ignorance". He is criticizing the idea that whatever has not been proven false must be true. "The Dragon in My Garage" is the same kind of statement about an invisible dragon in the garage that cannot be detected by any means.
If a theist is using this phrase to prove something about God they simply missed the point.
"The suppression of uncomfortable ideas may be common in religion and politics, but it is not the path to knowledge; it has no place in the endeavor of science." Carl Sagan
Carl Sagan said, "The fossil record implies trial and error, an inability to anticipate the future, features inconsistent with an efficient Great Designer." Carl Sagan "the absence of evidence is not evidence of absence" is giving evidence that there is no creator.
Caral Sagan also said, "Extraordinary claims require extraordinary evidence. For all I know we may be visited by a different extraterrestrial civilization every second Tuesday, but there's no support for this appealing idea. The extraordinary claims are not supported by extraordinary evidence."
Carl Sagan did not believe the stories about UFO's landing or UFO abduction stories because there was not compelling evidence. Nevertheless, Sagan was a proponent of the search for extraterrestrial life. He urged the scientific community to listen with large radio telescopes for signals from intelligent extraterrestrial life forms. He advocated sending probes to other planets. Sagan believed that the Drake equation suggested that a large number of extraterrestrial civilizations would form, but that the lack of evidence of such civilizations (the Fermi paradox) suggests that technological civilizations tend to destroy themselves rather quickly. This stimulated his interest in identifying and publicizing ways that humanity could destroy itself, with the hope of avoiding such destruction and eventually becoming a space-faring species. But the Drake equation was not based on the information we have today; it was based only on 400 billion stars we knew about in our galaxy at that time. Therefore, the possibility of extraterrestrial life is far greater than was predicted previously.
In "The Demon-Haunted World: Science as a Candle in the Dark" Sagan presented tools for testing arguments and detecting fallacious or fraudulent ones, essentially advocating wide use of the scientific method. He said, "The idea that God is an oversized white male with a flowing beard who sits in the sky and tallies the fall of every sparrow is ludicrous. But if by 'God' one means the set of physical laws that govern the universe, then clearly there is such a God. This God is emotionally unsatisfying - it does not make much sense to pray to the law of gravity."
When you start basing what is true on assumptions you wind up with religion.
"You cannot reason someone out of something they were not reasoned into."
Jonathan Swift