The Rare Earth Hypothesis argues that complex life is uncommon in the universe due to a combination of astrophysical/geological conditions that are rarely met. Hence, Earth is a one of a kind planet.
The Great Filter hypothesis suggests that all habitable planets go through filters in evolutionary development that most life forms don't survive (like asteriod collisions, geological changes) potentially explaining the scarcity of advanced extraterrestrial civilizations in the universe.
For the purposes of this debate, these are the only 2 hypotheses regarding the search for extraterrestrial life. Further, breakthroughs on either hypothesis are expected imminently.