This has long been a mystery, but a recent find at Qumran turned up a previously-unknown section of Megilat Ester and now it's clear. Well, pretty clear; the manuscript is a little hard to read because of all the wine stains.
The conspiracy of Bigtan and Teresh was bigger than first thought. There were two other conspirators, an Egyptian (צר, a shortened form of מִצְרָיִם) and Haman, their leader, who sought to eliminate Achashverosh and claim the throne.
It was quite ironic, then, that after Bigtan and Teresh were executed, the king promoted Haman to the #2 spot. But hey, the king was always kind of oblivious; Bigtan would have failed a security check had the king bothered to check the annals before hiring him, but he didn't. Haman was content to bide his time, but the Egyptian was rightly concerned that Haman would sacrifice his former conspirator at a moment's notice. After all, the guy was ready to start a major bloodbath over one guy not bowing down to him, and that stake was big enough for more than just Mordechai. Haman was clearly unstable and the צר would have to eliminate both Haman and Achashverosh before Haman eliminated him.
Now Ester wouldn't mind at all if the צר eliminated Haman, but she couldn't guarantee the outcome. The צר might first kill Achashverosh and then fail to kill Haman, and we'd end up with King Haman, a horrifying thought. So she warned the king about the צר who was coming for both of them, but since she knew that the king was pretty reckless (look how he treated Vashti), she focused on the threat to the king's trusted advisor instead of relying on his own self-interest. She hoped that, at the least, the צר would not have a vendetta against her people like Haman did. But in the best case, she hoped, when Achashverosh interrogated the man the truth would come out
and the king would remove both enemies.