Cortana is infected with the logic plague, caused by the Flood, but the Domain, a Precursor artifact, has given her knowledge of the Precursor/Flood’s true intention. All things in life will come to an end at the hands of the Precursors/Flood.
This is why she quotes: “If you knew how you were going to die, how would you live your life?” She is hinting that has acquired first hand information on how we were all destined to die. The Flood will wipe out all life in the universe, and serve it to the living universe, as intended by the Precursors. It’s not prophecy. It’s a cycle. That’s the true reason why the Forerunners waged war on them, because they learnt of their true intentions because they are so fowl and disgusting. Cortana has learnt of this too, and in her ascension she has attempted to bring forth the Forerunner army (and Guardians) once more, in a bid to fight the Flood and preserve life.
This is also an unstated reason why the Didact was attempting to wipe out humanity, not merely because of his hatred, but also because he knew of the Precursors plan. It wasn’t just about “the mantle”.