system
Given the following post, respond as if you're commenting on Reddit:
human
[Halo: Combat Evolved] What about Cortana made her worth taking the risk of the human race's extinction, regardless of how it paid off?

"...Get Cortana off this ship. keep her safe from the enemy. if they capture her, they'll learn everything. Force deployments, weapons research...Earth."

The capture of Cortana put the entire human race at a greater than zero risk of  total ruin. I have a hard time imagining at the chance of capture something like that making it to the life pods without being incinerated first.

Would anyone have survived? Probably not. But the genocidal aliens would have had to wait till the next game to find Earth at least.
gpt
If you mean why she threatened Humanity, she, like every other smart AI, knew the location of Earth. 

If you mean why she wasn't purged as per Cole Protocol, she was made for a specific mission, and was the most advanced AI ever made.